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FIELD MANUAL

GENERAL DRAFTING

HEADQUARTERS, DEPARTMENT OF THE ARMY

JANUARY 1 984

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ESSENTIALS

OF
DRAFTING

JAMES D. BETHUNE

Wentworth Institute
Boston, Massachusetts

PRENTICE-HALL, INC.

Eng/ewood Cliffs, New Jersey 07632

Library of Congress Cataloging in Publication Data

BETHUNE, JAMES D. (date)
Essentials of drafting.

Bibliography

Includes index.

1. Mechanical drawing. I. Title.
T353.B455 604\2 76-17056

ISBN 0-13-284430-3

All rights reserved. No part of this book may be reproduced in any form
or by any means without permission in writing from the publisher.

10 9 8 7

Printed in the United States of America

PRENTICE-HALL INTERNATIONAL, INC., London
PRENTICE-HALL OF AUSTRALIA PTY. LIMITED, Sydney
PRENTICE-HALL OF CANADA, LTD., Toronto
PRENTICE-HALL OF INDIA PRIVATE LIMITED, New Delhi
PRENTICE-HALL OF JAPAN, INC., Tokyo
PRENTICE-HALL OF SOUTHEAST ASIA PTE. LTD., Singapore
WHITEHALL BOOKS LIMITED, Wellington, New Zealand

To KENDRA

CONTENTS

Deface xu

Chapter J DRAFTING-TOOLS
AND THEIR USE

Introduction 2

2 Pencils, Leadholders, and Erasers

3 Scales 4

4 T-squares and Triangles 6

5 Compass 10

1-6 Protractors 11
1-7 Curves 12
1-8 Templates 13
1-9 Other Tools 14
Problems 16

Chapter 2 LINES AND LETTERS

2-1 Introduction 26
2-2 Kinds of Lines 26
2-3 Freehand Lettering 27
2-4 Guide Lines 28
2-5 Lettering Guides 29
Problems 30

Chapter 3 GEOMETRIC CONSTRUCTIONS

3-1 Introduction 36

3-2 Points and Lines 38

3-3 Add and Subtract Lines 39

3-4 Parallel Lines— First Method 40

3-5 Parallel Lines-Two Triangle Method 41

3-6 Bisect a Line— First Method 42

3-7 Bisect a Line— Second Method 43

3-8 Divide a Line Into Any Number of Equal

3-9 Divide a Line Into Any Number of Equal Parts

3-10 Fillets-Right Angles Only 46

3-11 Fillets-Any Angle 47

viii

Contents

3-12 Rounds— Any Angle 48

3-13 Hexagon— First Method 49

3-14 Hexagon— Second Method 50

3-15 Hexagon-Third Method 51

3-16 Hexagon-Fourth Method 52

3-17 Hexagon-Fifth Method 53

3-18 Pentagon— How to Draw 54

3-19 Pentagon— Definition 55

3-20 Octagon 56

3-21 Fillet-Two Circles 57

3-22 Round— Two Circles 58

3-23 Fillet— Concave Circle to a Line 59

3-24 Round— Convex Circle to a Line 60

3-25 S-Curve (Reverse or Ogee Curve) 61

3-26 Approximate Ellipse 62

3-27 Bisect an Angle 63

3-28 Parabola 64

Problems 65

Chapter 4 PROJ ECTION THEORY

4-1 Introduction 71

4-2 Orthographic Projections

4-3 Principal Plane Line 74

4-4 Points 75

4-5 Lines 77

4-6 Planes 80

4-7 Curves 82
Problems 84

Chapter 5

THREE VIEWS
OF AN OBJECT

5-1 Introduction 88

5-2 Normal Surfaces 88

5-3 Hidden Lines 90

5-4 Inclined Surfaces 94

5-5 Curved Surfaces 95

5-6 Sketching 97

5-7 Visualization Techniques
Problems 102

101

Chapter 6 DIMENSIONS

AND TOLERANCES

6-1 Introduction 112

6-2 Extension Lines, Dimension Lines,

Leader Lines, and Arrowheads 113
6-3 Locating and Presenting Dimensions 114
6-4 Unidirectional and Aligned Systems 123
6-5 Dimensioning Holes 123
6-6 Dimensioning Angles and Holes 124
6-7 Dimensioning Small Distances

and Small Angles 125
6-8 Base Line System 125
6-9 Hole-to-Hole System 126
6-10 Coordinate System 126

Contents j x

6-11 Tabular Dimensions 126

6-12 Irregularly Shaped Curves 128

6-13 Common Dimensioning Errors 128

6-14 Tolerances 128

6-15 Cumulative Tolerances 129

Problems 131

Chapter 7 OBLIQUE SURFACES
AND EDGES

7-1 Introduction 139

7-2 Compound Edges and Lines 139

7-3 Oblique Surfaces 144

1-A Parallel Edges 147

7-5 Dihedral Angles 149

7-6 Holes in Oblique Surfaces 153

7-7 Internal Surfaces in Oblique Surfaces 162

Problems 165

Chapter 8 CYLINDERS

8-1 Introduction 1 71

8-2 Cuts Above the Center Line 1 72

8-3 Cuts Below the Center Line 1 74

8-4 Inclined Cuts 176

8-5 Curved Cuts 1 78

8-6 Chamfers 181

8-7 Holes 184

8-8 Eccentric Cylinders 184

8-9 Hollow Sections 186

Problems 189

Chapter 9 CASTINGS

9-1 Introduction 195

9-2 Fillets and Rounds 195

9-3 Round Edge Representation 196

9-4 Runouts 197

9-5 Spotfaces and Bosses 198

9-6 Machining Marks 198

Problems 199

Chapter JO SECTIONAL VIEWS

10-1 Introduction 205

10-2 Cutting Plane Lines 206

10-3 Section Lines 208

10-4 Multiple Sectional Views 210

10-5 Revolved Sectional Views 211

10-6 Half Sectional Views 211

10-7 Broken Out Sectional Views 212

10-8 Projection Theory 213

10-9 Holes in Sectional Views 214

10-10 Auxiliary Sectional Views 214

10-11 Dimensioning Sectional Views 214

Problems 215

x Contents

Chapter 11 AUXILIARY VIEWS

11-1 Introduction 224

11-2 Reference Line Method 225

11-3 Projection Theory Method 228

11-4 Auxiliary Sectional Views 231

11-5 Partial Auxiliary Views 231

11-6 Secondary Auxiliary Views 232
Problems 241

Chapter 12 FASTENERS

12-1 Introduction 247

12-2 Thread Terminology 247

12-3 Thread Notations 248

12-4 Thread Representation 248

12-5 Threads in a Sectional View 253

12-6 Threads 254

12-7 Types of Bolts and Screws 255

12-8 Threaded Holes 255

12-9 Drawing Bolt and Screw Heads 258

12-10 Rivets 260

12-11 Welds 261

Problems 262

Chapter 13 METRICS

13-1 Introduction 267

13-2 The Metric System 267

13-3 Conversion Between Measuring Systems 268

13-4 Conversion Tables 269

13-5 First Angle Projections 272

Problems 274

Chapter 14 PRODUCTION DRAWINGS

14-1 Introduction 280

14-2 Assembly Drawings 280

14-3 Detail Drawings 282

14-4 Title Blocks 282

14-5 Parts List 283

14-6 Revision Blocks 283

14-7 Drawing Zones 284

14-8 Drawing Notes 284

14-9 One-, Two-, and Partial View Drawings 284

14-10 A Drawing Detail 287

14-11 Drawing Scales 287

14-12 Drilling, Reaming, Counterboring, and

Countersinking 288
Problems 290

Contents xi

Chapter 15 ISOMETRIC DRAWINGS

15-1 Introduction 297

15-2 Normal Surfaces 299

15-3 Slanted and Oblique Surfaces 302

15-4 Holes in Isometric Drawings 306

15-5 Round and Irregular Surfaces 311

15-6 Isometric Dimensions 315

15-7 Isometric Sectional Views 315

15-8 Axonometric Drawings 316

15-9 Exploded Drawings 317
Problems 318

Chapter 16 OBLIQUE DRAWINGS

16-1 Introduction 325

16-2 Normal Surfaces 327

16-3 Inclined and Oblique Surfaces 332

164 Holes in Oblique Drawings 335

16-5 Rounded and Irregular Surfaces 336

16-6 Dimensioning an Oblique Drawing 340

16-7 Oblique Sectional Views 341
Problems 341

Chapter 17 DEVELOPMENT DRAWINGS

17-1 Introduction % 348

17-2 Rectangular Prisms 348

17-3 Inclined Prisms 352

174 Oblique Prisms 354

17-5 Cylinders 357

17-6 Pyramids 362

17-7 Cones 367
Problems 370

Appendix A FINDING THE TRUE LENGTH OF A LINE
BY USING
THE REVOLUTION METHOD 374

Appendix B GAME PROBLEMS 376
Appendix C DRAFTING ART 377

Appendix D STANDARD

THREAD SIZES 378

BIBLIOGRAPHY 381
INDEX 382

PREFACE

This book has been written for the student who is taking drafting
either to satisfy a curriculum requirement or as an elective, but who is
not a drafting major. This student usually wishes to gain a basic working
knowledge of drafting fundamentals so that he can apply it to other
courses, but he is often hindered in obtaining this knowledge by a
combination of limited class time (basic drafting is normally a one
semester course) and large class enrollments. This situation forces the
student to rely heavily on the instructor's lectures and on his own
ability to read and understand the text.

To make it easier for the student to learn from this text, the
material is presented using a step-by-step problem-solving format ac-
companied by many illustrations. The written portion of the text may
be described as a "how to" approach. The idea is to present not only
drafting theory, but also the procedures and conventions used to apply
the theory. This will enable the student to work directly from the text
to the board while doing his class and homework drawings.

The scope of the material presented has been limited to those sub-
jects most often needed to prepare technical drawings, with heavy
emphasis on orthographic views (including sectional views and auxiliary
views) and dimensioning. Fasteners, oblique, isometric and develop-
ment drawings are also covered. Although limited in scope, the material
is presented in depth. Four chapters, for example, discuss how to draw
three views of an object.

Special care was taken in choosing exercise problems for each
chapter. The problems are directly related to the subject of the chapter,
and are, for the most part, presented in isometric form to help the stu-
dent learn visualization. Many are presented on grid background in
order to force the student to create all his own dimensions without any
hints or leads from dimensions used to state the problem. The problems
which are dimensioned are done so using decimals and the unidirec-
tional system, although most of the decimals are convenient fractional
equivalences.

The text also includes metrics. Chapter 13 is entirely devoted to
linear metric measurements (as used on technical drawings) and first
angle projection. All other chapters contain at least one exercise prob-
lem done in metrics.

Several people deserve my special thanks for their contributions
to this book. My wife, Kendra, not only did all the typing but also did
the initial editing for grammar and spelling errors. Chris Diincombe

Preface xiH

contributed his photographic skills to create interesting and imagina-
tive photographs. George Cushman, my colleague at Wentworth Institute,
was always willing to argue and discuss a method or teaching approach.
And Cary Baker and Stu Horton of Prentice-Hall always answered all
my questions promptly and clearly. Thanks to you all.

Finally, I would like to make a request of you, the reader. Please
send me your comments. A formal letter isn't necessary— just a marked
up xerox copy of the sections in question would be fine. Being a teacher
myself, I'm well aware that every text has certain sentences or illustra-
tions which, although not wrong, consistently cause confusion. I would
sincerely appreciate your pointing these out to me.

JAMES D. BETHUNE

Wentworth Institute
550 Huntington Avenue
Boston, Massachusetts

DRAFTING TOOLS
AND THEIR USE

Figure 1-0 Illustration courtesy of Teledyne Post, Des Plaines,
Illinois 60016.

1-1 INTRODUCTION

This chapter explains and demonstrates how to use basic drafting
tools. Most sections in the chapter are followed by exercises especially
designed to help you develop skill with the particular tool being pre-
sented. Try each tool immediately after reading about it by doing the
appropriate exercises. As you work, try to learn the capabilities and
usage requirements of each tool, because it is important that you know
how to use each tool with technical accuracy, skill, and creativity.

1-2 PENCILS, LEADHOLDERS,
AND ERASERS

Figure 1-1 shows several different pencils and leadholders. Most
draftsmen prefer to draw with leadholders instead of pencils because
leadholders maintain a constant weight and balance during use which
makes it easier to draw uniform lines.

4-r^

1 '

: ^BL ^

'7*™T" "' "^fc_

..:

■
Figure 1-1 Pencils and lead holders.

Sec. 1-2

Pencils, Leadholders, and Erasers

Regardless of whether a leadholder or pencil is used, its lead must
be kept sharp with a tapered, conical point like the one shown in
Figure 1-2. Figure 1-3 shows several different lead sharpeners and
Figure 1-4 shows how to sharpen a lead by using a sandpaper block.

When sharpening a lead, care should be taken to keep the graphite
droppings away from the drawing. Most draftsmen keep a cloth or
piece of clay handy to wipe the excess graphite from a newly sharpened
lead.

Leads come in various degrees of hardness, graded H to 9H. The
higher the number, the harder the lead. Light layout and projection
lines are usually drawn with the harder leads; darker lines, used for de-
tailing and lettering, are drawn with the softer leads.

Lead Holder's
Jaws

Lead

figure 1-2 The shape of a properly sharp-
ened lead.

1 *?v

Figure 1-3 Lead sharpeners.

Figure 1-5 shows several different kinds of erasers and an erasing
shield. The harder erasers are used for removing ink lines and the softer
ones are used for removing pencil lines. Gum erasers (very soft) are used
when large amounts of light erasing are required.

An erasing shield enables a draftsman to erase specific areas of a
drawing and thereby prevents excessive redrawing of lines that might
otherwise have been erased. To use an erasing shield, place it on the
drawing so that the area to be removed is exposed through one of the cut-
outs. (The various cutouts are shaped to match common drawing
configurations.) Hold the shield down firmly and rub an eraser into the
aligned cutout until the desired area is removed. When the erasing is
finished, the excess eraser particles should be brushed off. Figure 1-6
demonstrates the above method.

Figure 1 -4 Sharpening a lead using a sand-
paper block.

! >■■' ri- - '

Figure 1-5 Erasers and an erasing shield.

Figure 1-6 Using an erasing shield.

1-3 SCALES

Scales are used for linear measuring. Figure 1-7 shows a grouping
of several different kinds of scales. The scale most commonly used by
draftsmen is one with its inches graduated into 16 divisions with each
division measuring one-sixteenth of an inch. Figure 1-8 shows part of a
"16-to-the-inch" scale along with some sample measurements. Unlike
a real scale, the scale in Figure 1-8 has the first inch completely labeled
to help you become familiar with the different fractional values. Mea-
surements more accurate than one-sixteenth must be estimated. For
example, 1/32 is halfway between the and the 1/16 marks.

Figure 1-9 shows part of a decimal scale. Each inch is divided into
50 equal parts making it possible to make measurements within 0.01

! t

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Figure 1-7 Scales.

Sec. 1-3

Scales

-* t=

J_
16

7_
16

16 I 16

3-
1

1 32

!1
16

J5
15

* 2

Figure 1-8 A 16-to-the-inch scale with some sample measure-
ments.

.26

-* .14 -H

-.50

.37

-.73

1.04-

CM -tftOcO

qoo.o

too

Figure 1-9 A decimal scale with some sample measurements.

inch (hundredth of an inch) accuracy. Several sample readings have
been included and the first 0.10, unlike a real decimal scale, has each
graduation mark labeled.

Many scales are set up for other than '< full-sized drawing. For
example, the V* scale enables a half -sized drawing to be made directly
without having to divide each dimensional value by 2. Three-quarter
scales enable direct %-sized drawings to be made, and so on.

Drafting Tools and Their Uses

Chap. 1

HALF

15
16

3 -k

11
16

Figure 1-10 A half scale with some sample measurements.

All fractional scales are read as shown in Figure 1-10. Only one of
the sections representing an inch is graduated into fractional parts. This
graduated section is located to the left of the "0" mark. When making a
reading (for example, 3-7/8) on a fractional scale, read the whole (3)
part of the number to the right of the "0" and the fractional part (7/8)
to the left. See Figure 1-10 for an example of a 3-7/8 reading on a half
scale.

1-4 T-SQUARE AND TRIANGLES

A T-square is used as a guide for drawing horizontal lines and as a
support for triangles which, in .turn, are used as guides for drawing
vertical and inclined lines. Figure 1-11 shows a T-square and several
different sizes and types of triangles, including an antique wooden one.

Figure 1-11 T-square and triangles.

-: -, ".

Figure 1-1 2(a) Drawing a horizontal line using a
T-square as a guide.

Figure 1-1 2(b) Drawing a horizontal line using a
T-square as a guide.

To use a T-square or triangle as a guide for drawing lines, hold the
pencil as shown in Figures l-12(a) and l-12(b) and pull the pencil along
the edge of the straight edge from left to right. (These instructions are
for right-handed people. Left-handed people should reverse these direc-
tions.) Rotate the pencil as you draw so that a flat spot will not form
on the lead. Flat spots cause wide, fuzzy lines of uneven width. Always
remember to keep your drawing lead sharp.

When using a T-square, hold the head (top of the T) firmly and
flat against the edge of the drawing board. Use your left hand to hold
the T-square still and in place while you draw. When you move the T-
square, always check to see that the head is snug against the edge of the
drawing board before you start to draw again.

When a T-square and a triangle are used together to create a guide
for drawing, the left hand must not only hold the T-square in place; it
must also hold the edge of the triangle firmly and flat against the edge
of the T-square. To accomplish this, use the heel of your hand to hold
the T-square in place and your fingers to keep the triangle against the
T-square (see Figure 1-13).

It is important that all your tools be accurate. A T-square, for
example, must have a perfectly straight edge. If it does not, you' will
draw wavy lines and inaccurate angles with the triangles. To check a
T-square for accuracy, draw a long line by using the T-square as a guide.
Then flip the T-square over, as shown in Figure 1-14, and, using the
same edge you just used as a guide, see if the T-square edge (now upside-
down) matches the line. If it does not, the T-square is not accurate.
Triangles should be checked for straightness in the same manner
used to check a T-square, but, in addition, they must be checked for
"squareness." To check a triangle for squareness, align the triangle
against the T-square and draw a line by using the edge of the triangle
which forms a 90°-angle to the T-square as a guide. Holding the T-
square in place, flip the triangle over, as shown in Figure 1-15, and see
if the triangle edge matches the line. If it does not, the triangle is not

y*"

Figure 1-13 Drawing a vertical line using a
T-square and a triangle as a guide.

Figure 1-14 Measuring the following angles

Figure 1-15 Checking a triangle for squareness.

Sec. 1-4

T-Square and Triangles

square, meaning either that the 90°-angle is not 90°, or that the edge of
the triangle is curved, or that the edge of the T-square is curved.

To use the T-square and triangle as a guide for drawing a line
parallel to a given inclined line, align the long leg of the triangle with
the given line and then align the T-square to one of the other legs of
the triangle, as shown in Figure 1-16. By holding the T-square in place
with your left hand, you can slide the triangle along the T-square and
the long leg will always be parallel to the originally given line. You may
substitute another triangle in place of the T-square, as shown in Figure
L-17, and obtain the same results. Note that in either setup, the short
leg of the moving triangle is 90° to the long leg, meaning that you have
a guide not only for parallel lines, but also for lines perpendicular to
those parallel lines.

A T-square may be used in combination with a 30-60-90 triangle
and a 45-45-90 triangle to produce a guide for drawing lines which are
15° and 75° to the horizontal. Figure 1-18 illustrates how this is done.

Figure 1-16 Using a T-square and a triangle
as a guide for drawing inclined parallel lines.

Figure 1-17 Using two triangles as a guide
for drawing inclined parallel lines.

Figure 1-18 Using a T-square, a 45-45-90 triangle, and a 30-60-
90 triangle to draw lines 15° and 75° to horizontal.

|
_ ... |

j i i

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■

Figure 1-19 Compasses.

Figure 1-20 Setting a compass.

1-5 COMPASS

A compass is used to draw circles and arcs. The three basic kinds
of compasses are drop, bow, and beam. The bow is the most common

(SSe T^a^ompass, set the compass opening equal to the radius of
thP dPsired circle or arc by using a scale as shown in Figure 1-2U. men
otf he coTpL point directly on the circle center point and, using
lly one hanTand shown in Figures l-21(a) and l-21(b), draw m the
circle.

Figure l-2l(a) Drawing with a compass. Illustration courtesy of
Teledyne Post, Des Plaines, Illinois 6001o.

Figure l-21(b) Drawing with a compass.

■ :
■ . . .

Sec. 1-5

Compass

A compass lead must be sharpened differently from a pencil lead
since the compass lead cannot be rotated during use to prevent flat
spots from forming. Figure 1-22 shows how to sharpen a compass lead
and Figure 1-23 shows a close-up of a properly sharpened compass
lead.

1-6 PROTRACTORS

A protractor is used to measure angles. Figure 1-24 shows three
different kinds of protractors. The edge of a protractor is calibrated in-
to degrees and half degrees. Figure 1-25 shows part of a typical protrac-
tor edge along with some sample measurements. Measurements more
accurate than half a degree (0.5°) must be estimated.

To measure an angle, place the center point of the protractor on
the origin of the angle so that one leg of the angle aligns with the 0°
mark on the protractor. Read the angle value where the other leg of
the angle intersects the calibrated edge of the protractor.

i , •:=';. mi

Figure 1-22 Sharpening a compass lead.

Lead

Compass

■

Figure 1-23 The shape of a properly
sharpened compass lead.

Figure 1-24 Protractors.

Figure 1-25 A protractor with some sample measurements.

Drafting Tools and Their Uses

Chap. 1

1-7 CURVES

Curves are used to help draw noncircular curved shapes. Drafts-
men refer to them as French curves or ship's curves, depending on their
shapes (ship's curves look like the keel of a ship). Figure 1-26 shows a
grouping of curves.

Noncircular shapes are usually defined by a series of points and a
curve is used to help join the points with a smooth, continuous line.
Using a curve to help create a smooth line is difficult and requires much
practice Most students make the error of trying to connect too many
points with one positioning of the curve. Figure 1-27 shows a series of
points that are partially connected. The curve is in position to serve lis
a guide for joining only points 3 and 4-not 3, 4, and 5-even though all
three seem to be aligned. To join point 5 using the .shown curve posi-
tion would make it almost impossible to draw a continuous smooth
curve.

; 1 i

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Figure 1-26 Curves.

Figure 1-27 Aligning a curve with given points.

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■

Figure 1-28 Templates.

;

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■

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■

•

Figure 1-29 Circle templates.

1-8 TEMPLATES

Templates are patterns cut into shapes useful to a draftsman. They
save drawing time by enabling the draftsman to accurately trace a de-
sired shape. Some templates provide shapes that are difficult to draw
with conventional drawing tools (very small circles, for example).
Other templates provide shapes that would be tedious and time-con-
suming to layout and draw (ellipses, for example). Figure 1-23 shows a
sampling of templates.

The most common template used in mechanical drafting is the
circle template (see Figure 1-29). The holes of a circle template are

Drafting Tools and Their Uses

Chap. 1

r^r^tS I I,t Mk>*

Figure 1-30 Using a circle template.

labeled by diameter size and are generally made slightly oversized to
allow for lead thickness. Always check a circle template before initial
use to see if lead allowance has been included.

To use a circle template, locate the center point of the future
circle with two lines 90° to each other. Align the template with the two
90° lines by using the four index marks printed on the edge of the
template hole. Draw in the circle- Keep the leadholder vertical and
constantly against the inside edge of the hole pattern. Check the
finished circle with a scale. Figure 1-30 shows how to use a circle
template.

1-9 OTHER TOOLS

There are many tools, other than the ones already presented,
which are used to help create technical drawings. Figure 1-31, for
example, shows an adjustable curve ( t+ snake") which is very helpful
when drawing unusually shaped curves. Figure 1-31 also shows several

other tools.

Figures 1-3 2 (a) and 1-3 2(b) illustrate a drafting machine. A draft-
ing machine is a combination T-square, triangle, protractor, and scale
which, when used properly, will greatly increase drawing efficiency.
The information previously presented for using a T-square t triangle,
protractor, and scale may be directly applied to using a drafting ma-
chine. Check the manufacturer's instructions for the specific functions
of the machines.

Sec. 1-9

Other Tools

: . •

Figure 1-31 Magnifying glass, dividers, adjustable curve (snake),
tape, and brush.

Figure l-32(a) Using a drafting machine and an adjustable draw-
ing board. Illustration courtesy of Teledyne Post, Des Plaines
Illinois 60016.

Figure 1 -32(b) Using a drafting machine.
Illustration courtesy of Teledyne Post, Des
Plaines, Illinois 60016.

Drafting Tools and Their Uses

Chap. 1

PROBLEMS

1-1 (a) Measure the following lines to the nearest 1/16 of an inch:
(b) Measure the following lines to the nearest .01 of an inch:

1-2 Draw four 8"-lines as shown in Figure Pl-2. Make the lines very
light and very thin. Define the left end of each line as point 1.

~\ 1.00
2,50 1
4.00 I

5.50

1.00

^\ ^V H 4^

-.25 Border
all around

Figure Pl-2

Problems 17

Using point 1 as a starting point, measure off and label the fol-
lowing points:

Line 1

Line 2

Line 3

Distance

Value

1-2

1-3/8

1-3

1-9/16

1-4

2-1/4

1-5

2-7/8

1-6

3-21/32

1-7

1-8

5-3/8

1-9

5-3/4

1-10

6-5/16

1-11

7-15/16

Distance

Value

1-2

0.8

1-3

1.4

1-4

2.6

1-5

3.1

1-6

4.3

1-7

5.0

1-8

5,5

1-9

6.2

1-10

6.9

1-11

7.7

Distance

Value

1-2

0.38

1-3

1.25

1-4

2.44

1-5

3.06

1-6

4.22

1-7

5.00

1-8

5.50

1-9

6.13

1-10

6.94

1-11

7.88

Line 4 The values given must be reduced by a factor of 2

to fit on the line. Therefore, using a % scale, draw
the values.

Distance

Value

1-2

1.75

1-3

2.25

1-4

4.38

1-5

6.75

1-6

8.63

1-7

10.00

1-8

11.50

1-9

12.88

1-10

13.75

1-11

16.00

Drafting Tools and Their Uses

Chap. 1

1-3 Measure the following lettered distances to the nearest 1/16 of an
inch.

1-4 Measure the following lettered distances to the nearest .01 inch.

Problems

1-5 Redraw the following figure.

1-6 Redraw the following figure.

1-7 Redraw the following figure.

1-8 Redraw the following figure.

4.00

Drafting Tools and Their Uses

Chap. 1

1-9 Redraw the following figure.

1-10 Redraw the following figure. All dimensions are in
millimeters.

1-11 Redraw the following figure. Use only
a T-square, a 30-60-90 triangle, and a
45-45-90 triangle or a drafting machine.

^15°- 6 PL ACES

1-12 Redraw the following figure. The smallest circle is
1" in diameter and each additional circle is 1
larger in diameter up to 6" .

1-13 Redraw the following figure.

Problems

1-14 Redraw the following figure.

Figure PI -14 (a)

Figure PM4(b) Measure the following angles.

1-15 Redraw the following figure.

-^- TYPICAL

Drafting Tools and Their Uses

1-16 Redraw the following figure.
1 DJA

Chap. 1

r £ TYPICAL

( ^

r 1

i ' 4

-4-

3 *-

— 1

4 DIA

1-18 Redraw the following figure. Use a circle
template to draw in the rounded corners.

1-17 Redraw the following figure.

2 R
2 PLACES

8 PLACES

1-19 Draw two curves x versus y^ and x versus y 2 using the data points
provided. Use an axis system like the one presented and carefully
label each curve.

y 2

.00

2.00

.50

1.00

1.74

1.00

1.74

5.00

1.50

2.00

.00

2.00

1.74

-1.00

2.50

1.00

-1.74

3.00

.00

-2.00

3.50

- l.UU

-1,74

4.00

-1.74

-1.00

4.50

-2.O0

.00

5.00

-1.74

1.00

5.50

-1.00

1.74

6.00

.00

2.00

Problems
1-20 Redraw the following curve.

L-21 Redraw the following curve.

■24

Drafting Tools and Their Uses

Chap. 1

1-22 The following panel is part of a monocoque chassis design for a
dirt track motorcycle. It was created by Bob Gould and Peter
Morgan. Draw the panel on B-size (11 X 17) paper and use the V\
scale on your triscale. Label the finished drawing "Scale l A = 1."

2 PLACES

MATL
.125 7075-T6 AL

1-23 The performance data for the Yamaha 350RD pictured below is
given in the table provided. Plot the data, draw in the curves,
label each curve, and then write a short paragraph explaining
what the curves mean.

Engine Performance for Yamaha RD 350:

Engine Speed (rpm)

Horsepower (bhp)

Torque (ft-lb)

2000

6.0

15.0

3000

10.5

17.0

4000

15.0

19.5

5000

21.0

21.5

6000

29.0

25.0

7000

37.0

28.0

8000

36.5

23.0

9000

24.0

12.0

Figure Pl-23 Photograph courtesv of YAMAHA Corp.

DEPARTMENT OF THE ARMY

OFFICE OF THE ADJUTANT GENERAL
WASHINGTON. D.C. 20310

REPLY TO
ATTENTION OP

DAAG-PAP-A

SUBJECT: General Drafting, FM 5-553

TO: HOLDERS OF FM 5-553

6 January 1984

1. This commercial publication has been assigned Army publication number
FM 5-553 and supersedes TM 5-581A.

2. This publication provides a central source of information for the
technical drafting specialist, MOS 81B.

3. This letter will be permanently affixed to the book for the purpose of
authenticating its use as an official DA training publication.

BY ORDER OF THE SECRETARY OF THE ARMY:

Official:

ROBERT M. JOYCE

Major General, United States Army

The Adjutant General

JOHN A. W1CKHAM, JR.
General, United States Army
Chief of Staff

DISTRIBUTION:

Active Army, ARNG, USAR : To be distributed in accordance with Controlled
Distribution list.

LINES AND LETTERS

Figure 2-0 Illustration courtesy of Teledyne Post, Des Plaines,
Illinois 60016.

2-1 INTRODUCTION

This chapter deals with drawing some of the many different kinds
of lines used in technical drawings and deals with creating freehand let-
tering. Since each of these techniques will require a great deal of prac-
tice before proficiency is developed, don't be discouraged if your first
attempts seem shaky. The more you draw, the better your techniques
will become.

2-2 KINDS OF LINES

There are many kinds of lines commonly used on technical draw-
ings: visible, hidden, center, leader, and phantom to name but a few.
Each has its own specific configuration, thickness, intensity, and usage,
some of which are defined below. They are illustrated in Figure 2-1.
Those lines not defined in this chapter have a very specialized usage
which will be explained in conjunction with the subjects to which they
are related.

VISIBLE LINES: Heavy, thick, black lines approximately 0.020 inches
thick. Uniform in color and density. It may be helpful to draw object
lines with a slightly rounded lead in order to generate the necessary
thickness. To form a slightly rounded lead point, first sharpen the lead
and then draw a few freehand lines on a piece of scrap paper to take the
initial sharpness off the lead.
—Used to define the visible edges of an object
HIDDEN LINES: Medium, black, dashed lines approximately 0.015
inches thick. The dashes should be approximately four times as long as
the intermittent spaces. Hidden lines should be a little thinner and a
little lighter than visible lines.

—used to define the edges of an object which are not directly visible.
For further explanation, see Section 5-3.

LEADER LINES: Thin, black lines about 0.010 inches thick. Leader
lines should be noticeably thinner (about half as thick as visible lines).
To achieve the required line contrast, draw leader lines with a sharply
pointed lead.

—used to help dimension an object. For further explanation, see Sec-
tion 6-2.

CENTER LINES: Thin, black, lines drawn in a long line-space-short
line-space pattern approximately 0.010 inches thick. The long sections
may be drawn at any convenient length, but the short sections must be
approximately 1/8 long and the intermittent spaces should be approxi-
mately 1/16 long. Except for this configuration, center lines are identi-
cal to leader lines.

—used to define the center of all or part of an object. They are most
commonly used to define the center of holes. They may also be used to
help dimension an object.

Sec. 2-3

Freehand Lettering

Visible Line

Hidden Line

Leader Line

Center Line

Phantom Line

Figure 2-1 Five different types of lines commonly used on tech-
nical drawings.

PHANTOM LINES: Thin, black lines drawn in a long line-space-short
line-space-short line configuration approximately 0.010 inches thick.
The long sections may be varied in length, but the short lines must be-
1/8 longand the intermittent spaces should be approximately 1/16 long,
—used to show something that is relative to but not really part of a
drawing.

After you have studied Figure 2-1, try the exercises included at
the end of the chapter. Concentrate on line intensity and thickness and
on the contrast between the different kinds of lines. Intensity and
thickness are important, but equally important is that there be a notice-
able difference between the lines. For example, visible lines must be
approximately twice as thick as leader lines.

2-3 FREEHAND LETTERING

Figures 2-2 and 2-3 show the shape and style of the letters and
numbers most commonly used on technical drawings. Either the verti-
cal or inclined style is acceptable. The most widely accepted height for
letters and numbers is 1/8 or 3/16, although this may vary according to
the individual drawing requirements.

ABCDEFGHIJKLMNOPQRSTUVWXYZ
abcdefghijklmnopqrstuvwxyz

10TS56-4

0I23456789

Figure 2-2 Vertical letters and numbers.

28 Lines and Letters Chap. 2

ABCDEFGHIJKL M N P Q R S T U V W X Y Z
ab cd efg h ij klm n o p q rs tu vwxyz

0123456789

Figure 2-3 Inclined letters and numbers

When you are lettering, see that the lead is tapered and slightly
rounded at the tip. This differs from the tapered, sharp shape recom-
mended for drawing lines because it is easier to draw letters and num-
bers with a rounded point.

Also when you letter, use a softer lead (H or 2H) because it is
easier to letter with a soft lead than with a harder one. Since soft leads
tend to deposit excess amounts of graphite on the drawing, save let-
tering until the last phase of creating a drawing.

2-4 GUIDELINES

Guide lines are very light layout lines 1/8 or 3/16 apart (or what-
ever letter height is desired) which serve to help keep freehand lettering
at a uniform height. They may be drawn with the aid of a scale and T-
square or with the aid of a special guide line tool such as the Ames
Lettering Guide. Draftsmen sometimes draw their guide lines usmg a
nonreproducible blue pencil so that when the drawing is reproduced
the guide lines seem to have disappeared and only the letters or num-
bers remain. Figure 2-4 illustrates guide lines.

Draftsmen sometimes avoid putting guide lines on their drawings
by slipping a piece of graph paper, whose grid lines are the desired
distance apart, under the paper and then lettering within the grid lines.
This, of course, may be done only if you are working on a transparent
media.

i"i

lor A
8 16

Figure 2-4 Guide lines for lettering.

Sec. 2-5

Lettering Guides

IIJIJ— mWW.UlLlMUM

Figure 2-5 Creating guide lines for lettering by sliding a previ-
ously prepared set of parallel lines under the drawing paper.

If graph paper is not available or does not have the right size grid,
you may make your own guide line pattern on a, separate piece of paper
and then slide it under your drawing as was reconimended for the graph
paper. Figure 2-5 shows how this is done. Save the prepared guide line
pattern for future use.

2-5 LETTERING GUIDES

There are several different lettering guides that may be used to
create letters and numbers for drawings. By far the most widely used
guide for pencil work are the stencil kind shown in Figure 2-6.

When you use a lettering guide, support it with a rigidly held T-
square or other straight edge so that all the lettering is kept in the same
line. Use the same lead point shape described for use in freehand let-
tering (see Section 2-3).

Figure 2-6 Lettering guides.

^mmua&mmmmmBimmmssammtao^

10 Lines and Letters

PROBLEMS
2-1 Redraw the following figure.

Chap. 2

I 1

■ ! : i
i

Lb— — - 1

-*J U — -J- Typical,
! all aw

2-2 Redraw the following figure.

^ Typical

Problems

2-3 Redraw the following figure.

-y Typical

2-4 Redraw the following figure.

-1- Typical

~2 Lines and Letters

2-5 Redraw the following figure.

Chap. 2

ALL Lin0s are -1- apart

2-6 Letter the following notes.* Use the format illustrated in Figure
P2-6.

1. Right shown -left-sym. opp.

2. All inside bend radii are 2-times metal thickness unless other-
wise shown.

3. Mating surfaces must be coordinated with master die model of

parts as shown.

4. Same as 3431906 except as shown & use 3799034 w/wpr
motor decal in place of 3431908.

5 For inspection purposes, anchor hole at point A to set dimen-
sions specified, and check points B & C with 50# load applied
at point D in direction shown. Do not use tension spring
during insp. check.

6. Open tab for access to seat track attachment. Tab must be
closed after assy, of track (2-places).

7. Exceptions to PS4480-entire week may be coded with first
workday of that week.

8 The terminals shall not loosen or pull off their component
" assy at less than 15-lb effort applied to either terminal for
installation or removal of mating terminal.
9. For additional detail, see master model in Ornamentation
Studio Dept 6910.

*Courtesy of Chrysler Corporation.

Problems

10. Vendor must obtain location approval for gating & ejector
pms & dimensional approval of ejector pin bosses from mate-
rials laboratory engineering staff prior to construction

— Border - all around

Figure P2-6

2-7 Using the format shown in Figure P2-6, letter in the following
notes:* 6

1. Test per spec. P-72-B.

2. Paint black per spec. M-33.

3. Fan hood opening and fittings that fall on centerline of radi-
ator may vary ±0.06 from centerline.

4. "Ref" dimensions are for information only and therefore will
not be inspected per this print.

5. Permissible quality of hose fittings is 2% of outer diameter.

6. Finish: black paint per AM 6015 to withstand 96-hr salt
spray test per AM 6015 except finish on stainless steel flex-
ible blade to withstand 20-hr salt spray test.

7. All stamped identifications must be legible after painting.

8. Remove all fins & burrs.

9. Alternate balancing method: balance by drilling 0.33" dia.
max. holes in spider arms. The complete hole must be within
2 of the spider o.d. & the max. depth to drill point must be
0.125 .

'Courtesy of American Motors.

34 Lines and Letters Cha P- 2

10 Part no. & vendor identification (C.F.-RD-69597) to be
stamped in this area with 0.25" size letters X .010/.005 deep
on one or more arms & must appear on backside of fan blade
reinforcement cap. n

11. Valve must be fully open (.50 min stroke) at 8.0 ± .02 HG
vacuum signal on diaphragm.

12. Engineering approval of samples from each supplier is re-
quired prior to authorization of part production.

2-8 Using the format shown in Figure P2-6, letter in the following
information:*

Drafting Checking Guide

The following check list should be used as a guide in checking
drawings for compliance with related sections of Manufacturing
Standard S, Drafting Standards.

1. Does the general appearance of the drawing conform to Ford
Manufacturing Drafting Standards? Is the drawing clear, neat,
and thorough?

2. Have the proper sheet sizes been used?

3. Has the title block been filled in completely and is the infor-
mation correct? Are the title, scale, date, drawing and sheet
numbers, etc., correct? Is the title complete and clear? Does
the title include name of tools or equipment, operation or
product part name?

4. Is the ^rawing number correct and according to the proper
"Z" classification?

5. Are figures, letters, and lines correctly formed, uniform, and
clean? Are they sharp and dense enough to assure good repro-
duction and legibility?

6. Are the necessary views and sections shown and are they posi-
tioned in proper relation to each other?

7. Do witness lines extend to the correct surface?

8. Do arrowheads extend to the correct witness lines?

9. Are all necessary dimensions shown?

10. Are drawings and dimensions to scale?

11. Are dimensions which are not to scale underlined with a wavy
line, except those details with broken out sections?

12. Has duplication of dimensions and notes been avoided?

13. Are all components and included jobs shown in the stock list?

14. Has the assembly drawing been changed to agree with revised
detail drawing?

15. Are related "Z" and "S" numbered tools properly listed on
the main assembly drawings for reference?

16. On rework jobs are all changes fully and clearly listed?

17. Are cast details designed according to established practices?
See Group XB5.

2-9 Using the format shown in Figure P2-9, letter in the following
information. Place the first line of information directly over the
column headings and label each additional line above the previous
line.

- *Courtesy of Ford Motor Company.

As
Required

' .38

QTY

PART NO.

DESCRIPTION

-*-1.13-»-

-" 1.75—*-

QTY.

PART NO.

— 7.00 »*-|

DESCRIPTION

564S72

Housing

564S75

Cover Plate

663A46

Clips

100T01

Bracket

6-32 Screws

564S80

Side Support R.H,

564S85

Side Support L.H.

564S90

Base Plate

678Q99

Dowel Pins

Figure P2-9

2-10 Using the format shown in Figure P2-10, letter in the following
information.* Use your own initials under -the DR heading. Leave
the CK column blank.

< —

.75

h*-.8S*

6.13

, 1

J. 23 *■

' .33

i r

SYM

DATE

REVISION RECORD

Required

SYM.

DATE

REVISION RECORD

7/16/69

Optional Weight Revision

7/16/69

1.742/1.729 was 1.747/1.734

7/16/69

Note 8 Relocated

8/11/69

Issued

9/18/69

Released

5/12/70

See SF3210686 Rev A

10/21/70

Surface "J" Added

10/21/70

Notes 8 & 9 Added

10/21/70

Note Added

11/17/71

4 was 3

3/2/72

1.743/1.728 was 1.742/1.729

3/28/72

Was .005 T.I.R.

Figure P2-10

♦Information Courtesy of American Motors.

GEOMETRIC
CONSTRUCTIONS

3-1 INTRODUCTION

Geometric constructions are the building blocks of drafting. Every
drawing, regardless of its difficulty, is a composite of geometric shapes.
A rectangle is four straight lines and four right angles. A cam is a series
of interconnected arcs of various radii. Every draftsman must have a
fundamental knowledge of geometric constructions if he is to progress
to the more difficult format and layout concepts required by most
drawings.

This chapter is set up for easy reference. Each page contains one
method of doing one geometric construction. Both classical methods
and those requiring drafting equipment are presented. No attempt has
been made to avoid redundancy, and each method is completely
described within the page on which it is presented. A list of all construc-
tions described in this chapter is given below:

SUBJECT Page

3-1 Introduction 36

3-2 Points and Lines 38

3-3 Add and Subtract Lines 39

3-4 Parallel Lines— First Method 40

3-5 Parallel Lines— Two Triangle Method 41

3-6 Bisect a Line— First Method 42

3-7 Bisect a Line— Second Method 43

3-8 Divide a Line into Any Number of Equal Parts 44

3-9 Divide a Line into Proportional Parts 45

3-10 Fillets-Right Angles Only 46

3-11 Fillets— Any Angle 47

3-12 Rounds— Any Angle 48

3-13 Hexagon-First Method 49

3-14 Hexagon— Second Method 50

3-15 Hexagon— Third Method 51

3-16 Hexagon— Fourth Method 52

3-17 Hexagon— Fifth Method 53

3-18 Pentagon— How to Draw 54

Sec. 3-1 Introduction 37

3-19 Pentagon— Definition 55

3-20 Octagon 56

3-21 Fillet— Two Circles 57

3-22 Round— Two Circles 58

3-23 Fillet— Concave Circle to a Line 59

3-24 Round— Convex Circle to a Line 60

3-25 S-curve (Reverse or Ogee Curve) 61

3-26 Approximate Ellipse 62

3-27 Bisect an Angle 63

3-28 Parabola 64

Geometric Constructions

Chap. 3

3-2 POINTS AND LINES

A point, to a draftsman, is defined by the intersec-
tion of two construction lines.
Note:

A dot should not be used to define a point because
a dot may be easily confused with other marks on the
drawing and thereby cause errors.

Point

A line, to a draftsman, is an object line connecting
two or more points.

Note:

The accuracy of a curved line depends on the num-
ber points used to define it. The number of points used
depends on the accuracy required for the particular curve.

Line

Sec. 3-3 Add and Subtract Lines

3-3 ADD AND SUBTRACT LINES

Given : Line 1 -2 of length X and line 3 -4 of length

Problem: Add line 1-2 to 3-4.
1. Construct a line and define point 1 anywhere
along it.

Given: Line 1-2 of length X and line 3-4 of length
Problem: Subtract line 3-4 from line 1-2.

2. Using a compass set on point 1, construct an
arc of radius X.

3. Using a compass set on the intersection of the
arc constructed in step 2 and the line constructed in
step 1, construct an arc of radius R as shown. Line 1-4
is equal to line 1-2 plus line 3-4.

Construction Line

3. Using a compass set on the intersection of the
arc constructed in step 2 and the line constructed in
step 1, construct an arc of radius R as shown.

Line 1-4 equals line 1-2 minus line 3-4.

1. Construct a line and define point 1 anywhere
along it.

2. Using a compass set on point 1, construct an
arc of radius X .

Construction
Line

40 Geometric Constructions

3-4 PARALLEL LINES-FIRST METHOD

Chap. 3

Given: Line 1-2 and distance D.

r — *i^ D
i 1

Problem: Construct a line parallel to line 1-2 at
distance D.

2. Construct another arc of radius D as shown.

Any-
where along
Line 1-2

1. Using a compass set anywhere along line 1-2,
construct an arc of radius D as shown.

Anywhere along
Line 1-2

3. Construct a line tangent to both arcs.

Line parallel to Line1-2

Sec. 3-5

Parallel Lines— Two Triangle Method

3-5 PARALLEL LINES-TWO
TRIANGLE METHOD

™

Given: Line 1-2 and distance/).

Problem: Construct a line parallel to line 1-2 at
a distance D,

4. Construct a line along the edge of the 30-60-90
as shown.

5. Mark off a distance D from line 1-2 along the
line constructed in step 4.

1. Align the shortest leg of a 30-60-90 triangle
with line 1-2.

2. Place the hypothenuse of a 45-45-90 triangle
against the hypothenuse of the 30-60-90 triangle.

3. Holding the 45-45-90 triangle firmly and in
place, slide the 30-60-90 along the hypothenuse of the
45-45-90 as shown.

30-60-90

45-45-90

Slide the\
30-60-90

Hold firm
and in place

Construct

a line along

the edge of the

triangle
2

6. Realign the triangles to line 1-2 and slide the
30-60-90 until it is a distance D from line 1-2.

7. Construct a line along the shortest leg of the
30-60-90 through distance D parallel to line 1-2.

Note: °A T-square may be used in lieu of a second
triangle.

"The line used to locate distance D from
line 1-2 in step 5 is perpendicular to line
1-2.

42 Geometric Constructions

3-6 BISECT A LINE-FIRST METHOD

Chap. 3

Given: Line 1-2.

Problem: Divide line 1-2 into two equal parts.

1. Construct an arc of radius R. Use point 1 as

center.

R = any radius of greater length than Vi line 1-2.

center.

and 4.

2. Construct an arc of radius R. Use point 2 as

3. Define the intersection of the arcs as points 3

4 . Connect points 3 and 4 with a construction line.

5. Define point 5 where line 3-4 intersects line
1-2. Line 1-5 = line 5-2.

Note: This is the classical method as taught in
plane geometry.

Sec. 3-7

Bisect A Line— Second Method

3-7 BISECT A LINE-SECOND METHOD

Given: ne 1-2.

Problem: Divide line 1-2 into two equal parts.

2. Repeat step 1 this time constructing the 45°
line through point 2.

3. Define the intersection of the construction
lines as point 3.

Note: This method relies on drafting equipment
for completion. Any angle may be used in steps 1 and 2
as long as they are equal.

1. Align the T-square with line 1-2 and using a
45-45-90 triangle as a guide, construct a line 45° to
line 1-2 through point 1.

4. Draw a line through point 3 perpendicular to
line 1-2 which intersects line 1-2.

5. Define point 4 as shown. Line 1-4 = line 4-2.

Geometric Constructions

Chap. 3

3-8 DIVIDE A LINE INTO ANY
NUMBER OF EQUAL PARTS

Given: Line 1-2.

Problem: Divide line 1-2 into five equal parts.

2. Mark off five equal spaces along line 1-X and
construct a line 2-7.

Note: Any size space may be used as long as they
are all equal in length.

Note: This method is good for any number of
equal parts, not just for the five shown. Once 1-X has
been drawn, mark off as many spaces as needed. Re-
member that the spaces must be of equal length.

1. Construct a line A-X at any acute angle to
line 1-2.

3. Draw lines 6-F, b-E, 4-D, and 3-C parallel to
line 2-7.

1-C = C-D = D-E = E-F = F-2.

Sec. 3-9

Divide A Line Into Proportional Parts

3-9 DIVIDE A LINE INTO
PROPORTIONAL
PARTS

Given: Line 1-2.

1. Add up the total number of proportional parts
required and use the total derived as if the problem were
to divide the line into equal parts.

Problem: Divide line 1-2 into proportion*] parts
of 1, 3, and 5.

Any acute angle

1
3
5

See section 2. Divide a line into any number of
equal parts.

2. Mark off the required proportional parts.

9 Equal parts

Note: This method is good for any number of
parts and any ratio, not just for the 1,3, and 5 shown.

46 Geometric Constructi6ns

3-10 FILLETS-RIGHT ANGLES ONLY

Chap. 3

Given: Right angle and radius R.

+-=— r

Problem: Draw a fillet of radius R tangent to
angle 1-0-2.

3. Construct two more arcs of radius R. Use
points 3 and 4 as centers.

4. Define point 5 where, the arcs centered at
points 3 and 4 intersect.

1. Construct an arc of radius R. Use point as

center.

2. Define points 3 and 4 where the arc intersects
lines 0-1 and 0-2.

m 2

>J5. Draw a fillet of radius R. Use point 5 as center,
tangent to lines 0-1 and 0-2.

Note: 'This method is good only for right angles.

•For small radii, use a circle template and draw
fillet directly.

Sec. 3-11

Fillets— Any Angle

3-11 FILLETS-ANY ANGLE

Given: Angle 2-1-3 and radius R.

h-=H

Problem: Draw a fillet of radius R tangent to
angle 2-1-3.

2. Construct a line parallel to line 1-2 at a dis-
tance R.

3. Define the intersection of the two constructed
parallel lines as point 4.

1. Construct a line parallel to line 1-3 at a dis-
tance R,

4. Draw a fillet of radius R tangent to angle 2-1-3.

Note; -This method is good, not only for the right

angle as shown, but also for any angle, acute
or obtuse.

"For small radii, use a circle template and draw
the fillet directly.

48 Geometric Constructions

3-12 ROUNDS-ANY ANGLE

Chap. 3

Given: Angle 1-0-2 and radius R.
Problem: Draw a round of radius R tangent to
angle 1-0-2.

I 1

2. Construct a line parallel to line 0-1 at a dis>
tance R .

1. Construct a line parallel to line 0-2 at a dis-
tance R.

4. Draw a round of radius R. Use point 3 as center,
tangent to angle 1-0-2.

3. Define the intersection of the two constructed
parallel lines as point 3.

Sec. 3-1 3 Hexagon-First Method

3-13 HEXAGON-FIRST METHOD

Problem: Draw a hexagon D across the corners.

1. Construct a circle of diameter D.

., . Diameter ,.

Note: = radius. Set compass to radius

dimension. £

2. Using a compass, mark off six distances — as
shown. 2

_D
2

Start at any
point

Note: This is the classical geometric method and
is not generally used by draftsmen because it makes ,
positioning of the hexagon difficult.

-_ D

3. Draw in the hexagon.

50 Geometric Constructions

3-14 HEXAGON-SECOND METHOD

Chap. 3

Problem: Draw a hexagon S across the corners.

1. Construct a circle of diameter S.

Note: Diameter = radius. Set compass to radius
dimension.

3. Using points 2 and 3 as center, construct two
arcs of radius S/2.

2. Define points 2 and 3 as shown;

4. Define points 4, 5, 6, and 7 as shown.

5. Draw in the hexagon.

Sec. 3-15 Hexagon-Third Method

3-15 HEXAGON-THIRD METHOD

Problem: Construct a hexagon A across the cor-
ners.

1. Construct a circle of diameter A.

2. Using a 60°-triangle, construct lines 60° to
the horizontal as shown.

4. "Construct lines 1-2 and 3-4.

3. Define points 1, 2, 3, and 4.

5. Draw in the hexagon.

52 Geometric Constructions

3-16 HEXAGON-FOURTH METHOD

Chap. 3

Problem: Construct a hexagon B across the corners.
1. Construct a circle of diameter B.

2. Using a 30° -triangle, construct lines 30° to the
horizontal as shown.

4. Construct lines 1-2 and 3-4.

3. Define points 1, 2, 3, and 4.

5. Draw in the hexagon.

Sec. 3-17 Hexagon— Fifth Method

3-17 HEXAGON-FIFTH METHOD

Problem: Construct a hexagon C across the flats.

1. Construct a circle of diameter C.

3. Using a 30° -triangle, construct lines tangent to
the circle 30° to the horizontal as shown.

30 w to the
horizontal

2. Construct two vertical lines tangent to the circle.

C DIA

4. Draw in the hexagon.

54 Geometric Constructions

3-18 PENTAGON-HOW TO DRAW

Chap. 3

Problem: Draw a pentagon inscribed in a circle of
diameter A.

1. Construct a circle of diameter A.

2. Define points 0, 1, and 2 as shown.

3. Bisect line 0-1 and define the midpoint
as point 3.

4. Define point 4 as shown.

5. Using a compass set on point 3, construct an
arc through point 4 and line 2-0.

6. Define the intersection of the arc constructed
in step 5 and line 2-0 as point 5.

8. Define the intersection of the arc constructed
in step 7 and the circle as point 6.

7. Using a compass set on point 4, construct an
arc through point 5 and the edge of the circle.

9. Using a compass, mark off the distance 4-6
around the circumference of the circle as shown.

10. Draw in the pentagon.

Sec. 3-1 9 Pentagon— Definition

3-19 PENTAGON-DEFINITION

Define a pentagon

— 7?

1.1 7558 R

Note: This information has been included as a
reference to help in drawing pentagons.

Geometric Constructions

Chap. 3

3-20 OCTAGON

Problem : Draw an octagon D across the flats.
1. Draw a circle of diameter D.

2. Construct four tangent lines as shown.

D DIA

3. Construct four lines, 45° to the horizontal,
tangent to the circle as shown.

^— 45 v to the
horizontal

4. Draw in the octagon.

Sec. 3-21 Fillet-Two Circles

3-21 FILLET-TWO CIRCLES

Given: Circles X and Y and radius R.

H h

1. Construct an arc of radius X + R. Use point 1
as center.

x+R

Problem: Draw a fillet of radius R tangent to
circles X and Y.

2. Construct an arc of radius Y + R. Use point 2
as center.

y+R

(See Section 3-3, Add and Subtract Lines.)

4. Using point 3 as center, draw a fillet of radius
R tangent to the two circles.

3. Define the intersection of the two arcs as point 3.

58 Geometric Constructions

3-22 ROUND-TWO CIRCLES

Chap. 3

Given: Circles x and y and radius R.
Problem: Draw a round of radius R tangent to
circles x and y.

2. Construct an arc of radius R-y. Use point 2 as
center.

3. Define the intersection of the two arcs as
point 3.

R-y

1. Construct an arc of radius R-x> Use point 1
as center.

(See Section 3-3, Add and Subtract Lines.)

R-x

4. Using point 3 as center, draw an arc of radius
R tangent to the two circles.

Sec. 3-23

Fillet— Concave Circle To a Line

3-23 FILLET-CONCAVE CIRCLE
TO A LINE

Given: A circle of radius X t line 1-2, and a radius

Problem : Draw a fillet of radius R tangent to a
circle and a line.

2. Construct a line parallel to line 1-2 at a dis-
tance R.

3. Define the intersection of the arc (X + R) and
the line parallel to line 1-2 as point 4.

1. Construct an arc of radius X + R. Use point 1
as center.

X+R

4. Using point 4 as center, draw in a fillet of
radius R.

Geometric Constructions

Chap, 3

3-24 ROUND-CONVEX CIRCLE
TO ALINE

Given: Circle x, line 1-2, and fillet radius R.

1. Construct a circle of radius x - R.

Problem: Draw a round tangent to a circle of
radius x and line 1-2.

2. Construct a line parallel to line 1-2 at a dis-
tance R.

3. Define the intersection of the circle (x - R)
and the line parallel to line 1-2 as point 3.

x-R
(radius)

(See Section 3-3, Subtracting Lines)

4. Draw a round of radius R. Use point 3 as center.

Sec. 3-25

S-Curve (Reverse or Ogee Curve)

3-25 S-CURVE (REVERSE OR
OGEE CURVE)

1. Construct line 1-2.

2. Divide line 1-2 into four equal parts.

3. Construct perpendiculars from points 1 and 2
such that they intersect the quarter bisect lines as shown.

4. Define the intersects of step 3 as points 3 and 4.

Note: The S-curve need not be symmetrical. Asym-
metrical curves may be constructed, but the method is
not covered in this book.

5. Using points 3 and 4 as centers, draw in curves
of radii 3-1 and 4-2.

Geometric Constructions

Chap. 3

3-26 APPROXIMATE ELLIPSE

Given: A major axis of A-O-B and a minor axis of

x-o-y

Problem: Construct an approximate ellipse.

1 Draw an arc of radius 0-A. Use point as a
center such that it intersects point A and an extension of
line y-O-X.

2. Draw a straight line between points X and tf.

3! Draw arc X-2 as shown.

4. Define the intersection of arc (X-2) and line
X'B as point 3. . . Y— 2

5. Bisect line 3-5 and draw the bisect line so
that it intersects an extension of the line X-O-y. Define
this intersection as point 5.

Bisect of
line 3-B

4-B

6. Define the intersection of the bisect line and
line 0-B as point 4.

7. Using point 5 as center, draw an arc of radius
5-X as shown. Also draw an arc of radius 4-B as shown.
These two arcs will generate half of ellipse. Draw the
half by symmetry.

Sec. 3-27 Bisect an Angle

3-27 BISECT AN ANGLE

Given: Angle 1-0-2

Problem: Bisect angle 1-0-2.

2. Define points 3 and 4 where the arc intersects
lines 0-1 and 0-2.

4. Define the intersection of the two arcs as
point 5.

center.

1. Construct an arc of radius R. Use point as

3. Using points 3 and 4 as centers, construct two
more arcs of radius R m shown.

5. Construct a line 0-5,

Angle 1-0-5 = Angle 5-0-2.

Geometric Constructions

Chap. 3

3-28 PARABOLA

Problem: Draw a parabola whose major axis is
twice the minor axis.

Major Axis

Minor Axis

2. Construct lines from the first point on the ma-
jor axis to the last point on the minor axis, etc. (1-10,
2-9,3-8,4-7, 5-6)

3. Define points 11, 12, 13, and 14 as shown.

Note: "In this example the major axis points are V6
apart and the minor axis points are V* apart.
•The accuracy of the parabola depends on the
number of points used to define it. The more
points, the greater the accuracy.

1. Lay out points making those on the major axis
twice as far apart as those on the minor axis.

o' & 7' tf wtd

The number of points on each axis must be equal.

4. Draw a parabola by using a French curve and
connecting points 5-11-12-13-14-10.

1 6 l T 3

Problems 0*

PROBLEMS

3-1 You are given a line 1-15/16 long. Bisect it.

3-2 You are given a line 2.36 long. Bisect it.

3-3 Draw two parallel lines 15/16 apart.

3-4 Draw two parallel lines VA apart.

3-5 Draw two parallel lines 2.063 apart.

3-6 You are given a line 2-1/8 long. Divide it into 7 equal parts.

3-7 You are given a line 3 l 4 long. Divide it into 15 equal parts.

3-8 You are given a line 1.68 long. Divide it into 3 equal parts.

3-9 You are given a line 1-7/8 long. Divide it into proportional
parts of 2, 4, and 7.

3-10 You are given a line 2-9/16 long. Divide it into proportional
parts of 1, 4, 3, and 5.

3-11 You are given a line 2.78 long. Divide it into proportional parts
of 3, 4, and 9.

3-12 You are given lines of 1-1/16 and 5/8 long. Graphically add them.
3-13 You are given lines of 1.75 and 0.625 long. Graphically add them.

3-14 You are given a line 2-3/8 long. Subtract a line 1-3/16 long from

it.

3-15 You are given a line 1-7/8 long. Subtract a line 15/16 long from it.

3-16 You are given a line 1.28 long. Subtract a line 0.80 long from it.

3-17 You are given a 37° angle. Draw a fillet of radius %.

3-18 You are given a 123° angle. Draw a fillet of radius 1-3/8.

3-19 You are given a 90° angle. Draw a round of radius 7/8.

3-20 You are given a 60° angle. Draw a round of radius 1.20.

3-21 Draw a hexagon VA across the comers.

3-22 Draw a hexagon 2-3/16 across the corners.

3-23 Draw a hexagon 1.80 across the corners.

3-24 Draw a hexagon 80 mm across the corners.

3-25 Draw a hexagon 2 across the flats.

3-26 Draw a hexagon 2-9/16 across the flats.

3-27 Draw a pentagon inscribed within a 2% diameter circle.

3-28 Draw an octagon inscribed within a 1-7/8 diameter circle.

3-29 You are given two circles of VA and 7/8 in diameter and located
VA apart. Draw a fillet between them of radius %.

3-30 You are given two circles of 1.75 and 1.10 in diameter and lo-
cated 1.60 apart. Draw a fillet between them of radius .90.

Geometric Constructions

Chap. 3

3-31 You are given two circles of 1V4 and 1V4 in diameter and located
2V4 apart. Draw a round between them of radius 2V6.

3-32 You are given a circle 1-7/16 in diameter located 2-1/8 above a
line. Draw a fillet between them of radius 1-1/16.

3-33 You are given a circle 2% in diameter located 9/16 above a line.
Draw a round between them of radius 7/8.

3-34 Draw an approximate ellipse with a minor axis of 1 and a major
axis of IV2.

3-35 Draw an approximate ellipse with a minor axis of 2.25 and a ma-
jor axis of 3.80.

3-36 Draw a parabola whose major axis is l l A times the minor axis.

3-37 Draw a parabola whose major axis is two times the minor axis.

3-38 You are given an angle of 60°. Bisect it.

3-39 You are given an angle of 50°. Bisect it.

3-40 You are given an angle of 108°. Bisect it.

3-41 You are given an angle of 42.5°. Bisect it.

Redraw the following shapes:

3-43

.50 01 A
4 PLACES

2.75 DIA

4.00

1.13R

1.13 DIA

Problems

1.30 a

2.00R

.88 R

3-45

1.13 n

3.00 R

8101 A

75 H

STRAIGHT
LINE

.75 R
2 PLACES

3-46 Use B size paper.

75R
2 PLACES

1.25DIA

1.38 R

1.75 01 A

5.00

3-47

.94 DIA

1,75 R

Geometric Constructions

3-48

Chap. 3

75 R-2 PLACES

1.60R

3-49

2.88

,50 DIA
5 PLACES

.73 fl
TYPICAL

,19R

P3-*t^

2.75R

HEXAGON!
20 ACROSS
THE FLATS

3-50 Millimeters.

4 PLACES

Problems

3-51 Use B size paper.

.50 R
2 PLACES

.25 R
5 PLACES

1.38DIA-

2.00-

.380IA-

810IA

4.00

2.00

1.00

3.81 *-

5.19

8.00

PROJECTION THEORY

sr^;-" ,, '*-;

Figure 4-0 Many views of an object are needed to present a clear
idea of the object's shape. Photograph courtesy of General Motors
Corp.

4-1 INTRODUCTION

The purpose of a technical drawing is to communicate information.
As in any kind of communication, it is easy to know what you want to
say but sometimes very difficult to make yourself understood.

From the time a customer places his initial order until the finished
product is delivered, many people of varying technical skills and back-
grounds will contribute to help satisfy the demands of the order. An
engineer and draftsman design the product and prepare the necessary
drawings. The drawings are then used progressively by a planner to
price and time the job, by a buyer to order necessary manufacturing
stock, by a shop foreman to schedule and assign the work, by a machin-
ist to actually make the parts, by an inspector to make sure that the
work has been done properly, by an assembler to put the pieces to-
gether, by another inspector, and so on. Each member of this hypo-
thetical chain takes from the drawings information that he needs for
his particular function. It is, therefore, easy to see why the drawings
must be accurate and clear, free from ambiguities or misleading repre-
sentations. Just as the years of written communication have led to
rules and conventions, so years of manufacturing and production
experience have led to drafting rules and conventions that help prevent
errors.

4-2 ORTHOGRAPHIC PROJECTIONS

One of the most useful systems used by draftsmen to help assure
accurate communication is orthographic projection.

Orthographic projections are views of an object taken at right angles to
the object and arranged in specific relative positions on the drawing.

There is an infinite number of possible orthographic projections— there
is an infinite number of ways to look at an object— but the views most
commonly used are front, top, bottom, right side, left side, and rear
(see Figure 4-1).

Six views are not generally required, for most objects may be
completely 'defined in three views: front, top, and right (corresponding
to height, width, and depth). Drafting convention calls for these views
to be specifically placed on a drawing, and any variance is an error.
Figure 4-2 shows the three views in correct position. Figure 4-3 shows
two examples of positioning errors.

Each orthographic view is taken at right angles to the object it is
defining. It is not a picture, such as an artist would draw, but a two-
dimensional representation which, for the sake of technical accuracy,

Projection Theory

Chap. 4

Top

Front

Rear

Bottom

Figure 4-1 A front, top, bottom, right side, left side, and rear
views of an object.

Top

Front

SJdo

Figure 4-2 Three views of an object located in correct relative
positions.

Sec. 4-2

Orthographic Projections

Front

Figure 4-3 Orthographic views which are not positioned correctly.

has given up perspective. There is no shading and no attempt to "pic-
ture" the object. Each view presents only one face or one piece of the
total information. Orthographic views are dependent on each other for
a complete definition of the object. (There are objects that require
fewer than three views, but these will be covered later.) In the top view
in Figure 4-4, which surface is higher? There is no way to tell from this
one orthographic view. Other views are needed before an answer may
be given.

Top View

Figure 4-4 Given a top view of an object, which surface is
higher? Other views are needed before an answer can be formu-
lated.

Projection Theory

Chap. 4

4-3 PRINCIPAL PLANE LINE

Drawings are divided into zones. Each zone contains one ortho-
graphic view along with all information pertinent to that view. The
zones are separated by crossed (at 90°) construction lines called princi-
pal plane lines which are similar to a mathematical coordinate system.
They are omitted on most finished drawings, but their presence is tacit.
They will be included for the first problems in order to help establish
the importance of the separation and relative position of views.

Principal plane lines are defined in Figure 4-5(a). Figure 4-5(b)
shows how principal planes lines were initially developed.

Figure 4-5(a) Principal plane lines.

TOP view
zone

Front

FRONT view
zone

Right

Side

Front

Principal

Plane Lines

RIGHT SIDE view
zone

Right

Side

Front

Figure 4-5(b) How principal plane lines were initially developed.

Principal
Plane Lines

Right
Side

Sec. 4-4

4-4 POINTS

Points

Projection theory is the study of how to transfer information from
one orthographic view to another. Often, two views of an object may
be visualized, or parts of each view may be drawn, but the completed
drawing remains clouded. Projection theory enables the bits and pieces
to be used together to arrive at a finished drawing.

Reduced to its simplest form, projection theory may be used to
transfer a single point from one view to another. Figure 4-6 presents
the problem of finding the right side view of a point where the front
and top views are given. Figure 4-7 shows the solution.

GIVEN: Front and top views of point 1.
PROBLEM: Draw the side view of point 1.

Top

Front

Right Side

Figure 4-6 Top and front views of point 1.

SOLUTION:

Mitre Line (at 45°)

-f"

Figure 4 -7 (a)

RIGHT SIDE view
of point 1

Figure 4-7(b)

Projection Theory

Chap. 4

1. Project the front view of point 1 into the right side view zone.
This is done by drawing a horizontal construction line parallel
to the horizontal principal plane line. The tendency here is to
draw the projection line too short meaning extension may be re-
quired later on. All we know at this time is that the right side
view is somewhere along the projection line.

2. Draw a line 45° up and to the right from the intersecting point
of the principal plane lines. This is called a mitre line.

3. Project the top view of point 1 into the right side view zone.
This is done by drawing a horizontal construction line to the
right, parallel to the horizontal principle plane line until it
touches the 45° -mitre line. When the projection line touches
the mitre line, it turns the corner, Le. t it goes from horizontal
to vertical- To continue the projection line, draw a vertical
construction line, parallel to the vertical principal plane line,
extending down into the right side view zone. As in step 1,
don't be stingy with the lead; draw the projection line through
and beyond the horizontal projection line.

4. The intersection of the two projection lines is the right side
view of point 1. Label it.

Several additional points should be made before leaving this prob-
lem. The location of the front view of point 1 in relation to the top
view is not random. The vertical line between the front and top views
is parallel to the vertical principal plane line. Figure 4-8 shows three
views of point 1 and the projection lines used to go from view to view.
The point views and lines form a perfect rectangle (a four-sided figure
with four right angles). This projection rectangle enables the draftsman
to find any third view of a point when he is given the two other views.
This means that if we consider only three principle views (top, front,
and right side), there are only three possible projection problems.

TOP— RIGHT SIDE

FRONT — TOP

RIGHT SIDE — FRONT

Figure 4-8 Projection rectangle.

Sec. 4-5

Lines

1. When you are given the front and top, draw the right side.

2. When you are given the front and right side, draw the top.

3. When you are given the top and right side, draw the front.

The sample problems in Figures 4-9 and 4-10 are examples of the other
two possible point projection problems. Study them before proceeding
to the next section.

GIVEN: Top and right side views of point 2.
PROBLEM: Draw front view.

GIVEN: Front and right side views of point 3.
PROBLEM: Draw top view.

SOLUTION:

TOP view-
of point 3

SOLUTION:

FRONT view
of point 2

Figure 4-9

Figure 4-10

4-5 LINES

The projection of lines between views follows directly from point
projection theory if we consider the axiom:

To a draftsman, a line is a visible line that connects two
or more points.

Axiom 4-1

It follows then that lines may be projected by projecting the points
that define them.

Figure 4-11 presents the problem of finding a right side view when
the front and top views are given. Figure 4-12 is the solution and was
arrived at by the following:

1. Projecting point 1 into the right side view (see Figure 4-1).

Projection Theory

Chap. 4

GIVEN: Front and top views of line 1-2.
PROBLEM: Draw side view.

^~2

Figure 4-11

SOLUTION;

Figure 4-12(a)

Figure 4-1 2(b)

Sec. 4-5

Lines

2. Projecting point 2 into the right side view.

3. Connecting points 1 and 2 with an object line.

Step 3 is the right side view of line 1-2.

One aspect of line projection that could cause confusion is a double-
point projection. This is clarified by the following axiom:

The end view of a straight line is a point (really a double
point).

Axiom 4-2

Figure 4-13 is an example of a double-point projection. The solu-
tion is derived exactly as shown in Figure 4-11, except for step 3.
Points 1 and 2 cannot be joined by an object line because the line ex-
tends into the paper and therefore appears as a double point. This may
be visualized if you hold a pencil horizontal to the ground and rotate
it until you are looking directly at the point with the eraser end directly
behind the point. If the point represents point 1 and if the eraser repre-
sents point 2, you now have a model of the end view of a line.

Figures 4-14, 4-15, and 4-16 are samples of solved line projection
problems. Study them before proceeding to the next section.

GIVEN: Front and top view of line 5-6.
PROBLEM: Draw right side view.

S H h 6

GIVEN: Front and right side views of line 4-5.
PROBLEM: Draw top view.

SOLUTION:

RIGHT SIDE view
of line 5-6

*\ * M

"5 r 5

Figure 4-13 End view of a line.

Figure 4-14

Projection Theory

Chap. 4

GIVEN: Front and right side view of line 8-9.
PROBLEM: Draw top view.

GIVEN: Top and right side views of line 7-8.
PROBLEM: Draw front view.

SOLUTION:

TOP view
of line 8-9

SOLUTION:

Figure 4-16

4-6 PLANES

As line projection theory was derived from point projection theory,
so plane projection theory follows directly from line projection theory
if we consider the following axiom:

To a draftsman, a plane is the area enclosed within a
series of lines interconnected end to end.

Axiom 4-3

This differs from the geometric concept of planes in that it con-
siders a plane a finite area, that is, an area with known boundaries.

Figure 4-17 gives the front and top views of plane 1-2-3-4 and
asks for the right side view. Figure 4-18 shows the solution which was
arrived at by the following:

1. Identify the lines that define the plane 1-2, 2-4, 4-3, and 3-1.

2. Project the individual points 1, 2, 3, and 4 into the right side
view (see Figure 3-7),

3. Draw in with object lines the lines that define the plane.

The lines drawn in step 3 define the right side view of plane 1-2-

3-4.

Sec. 4-6

Planes

GIVEN: Front and top views of plane 1-2-3-4.
PROBLEM: Draw right side view.

SOLUTION:

Figure 4-17

Figure 4-18

In line theory we found that the end view of a line was a double
point. A similar situation appears in plane theory which is explained
by the following axiom:

The end view of a plane is a line (really several lines
directly behind each other).

Axiom 4-4

This may be verified by holding a sheet of paper horizontal to the
ground and rotating it until you are looking directly at one edge. Al-
though it is a plane, the sheet appears as a line.

Figure 4-19 is a sample problem involving the end view of a
plane. Points 1, 2, 3, and 4 are double points or end views of lines.
Line 1-3 is located directly behind line 2-4 and is therefore hidden
from view. Figure 4-19 is a good example of why orthographic views
are dependent on each other to present a complete picture of an ob-
ject. By itself, the right side view is not only incomplete, it is also mis-
leading.

GIVEN: Front and top views of plane 1-2-3-4.
PROBLEM: Draw the right side view.

Figure 4-19

SOLUTION:

Projection Theory

Chap. 4

4-7 CURVES

So far we have considered only straight lines. Point, line, and plane
projection theory may be extended to include curved lines if we con-
sider the following axioms:

To a draftsman, a curved line is a visible line connecting
three or more points which form a smooth, nonlinear
line. Axiom 4-5

To a draftsman, the accuracy of a curve is a function of

the number of points used to define the curve. Axiom 4-6

To draw a perfectly accurate curve would require an infinite num-
ber of points. To do this is not only impossible, it is also impractical.
Most curves may be very closely approximated by a finite number of
points, and it is up to the draftsman to determine which level of ac-
curacy is required and how many points he needs to achieve this level.
Circles and perfect arcs are exceptions to the axioms because they may
be drawn with perfect accuracy by using a compass.

Figures 4-20 and 4-21 are examples of curved line projection prob-
lems and Figure 4-22 is an example of a plane with a curved edge. The
solution to each of these problems is based on the concept of point
project theory as shown in Figures 4-7, 4-9, and 4-10.

GIVEN: Front and right side views of curved line 1-2.
PROBLEM: Draw top view.

Figure 4-20

Curves

1 -

He —

l 3 >

I J

-^tr -■

~*Y

\/ A

2 ST

Figure 4-21(a)

Figure 4-21(b)

GIVEN: Front and top views of plane 1-2-3-4-5
PROBLEM: Draw the aide view.

P*«

SOLUTION:

1 2

5 4 J

(

t
r^..g

-ii"

5 4 4,5

)

Figure 4-22

Projection Theory

PROBLEMS

Chap. 4

Draw three views (front, top, and side) of the following points, lines,
and planes. Include principal plane lines, mitre lines, and projection
lines for each problem. Each square on the grid is 0.20 X 0.20.

4-1

13;

4*5i

Tl|L

EflOL.

F.^nt

4-2

Tlfl

13 tf

i-Aitr:

san*:

IE:

Problems

4-3

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4-5

Projection Theory

Chap. 4

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THREE VIEWS
OF AN OBJECT

Figure 5-0 A front view of a BMW R90S. Photograph courtesy
of Bob Braverman's Cycle Rider Publications, Inc.

5-1 INTRODUCTION

In this chapter we will extend the projection theory concepts of
Chapter 4 to cover three-dimensional objects. The basic three views
(front, top, and right side) and their relative locations on the drawing are
the same for three-dimensional objects as they are for points, lines, and
planes. Similarly, the techniques for projecting information from one
view to another remain exactly the same. As we consider lines to be
defined by points and we consider planes to be defined by lines, so we
may consider three-dimensional objects to be defined by planes and,
therefore, directly apply projection theory.

We also introduce in this chapter the concept of object visualiza-
tion. Object visualization is the ability to mentally picture an object in
three dimensions when only orthographic views are given and to men-
tally visualize the orthographic views of an object when only a three-
dimensional picture is given. It is an important skill for a draftsman to
develop. Each sample problem in this and the next six chapters will
include both the orthographic views and a three-dimensional drawing,
called an isometric drawing, of the objects to be studied so that an
understanding of the object visualization may be developed.

5-2 NORMAL SURFACES

Figure 5-1 shows an object and a three-view orthographic drawing
of that object. All surfaces in the object are normal, that is, at 90° to
each other. The principal plane lines and the projection lines have been
included, and points 1, 2, 3, 4, 5, and 6 have been defined.

Figure 5-1 An object and a three view orthographic
drawing of that object.

Sec. 5-2

Normal Surfaces

Figure 5-2 An object and a three view orthographic drawing of
that object.

Planes 1-2-3-4 and 2-3-5-6 have been numbered to demonstrate
the application of projection theory to objects. Projection theory is
directly applicable to three-dimensional objects if we consider the fol-
lowing axiom:

To a draftsman, an object is a volume enclosed within a
series of interconnected planes.

Axiom 5-1

As we are able to analyze lines from points and analyze planes
from lines, so we are able to analyze objects from planes. Planes 1-2-3-4
and 2-3-5-6 are analyzed separately in Figure 5-2. All other surfaces
that make up the object may be analyzed in the same way and then
combined into a composite of planes which in turn form the three
views of the object.

Normally, a draftsman does not number all points on an object
because he mentally sees his finished drawing before he draws it. This
is not always true, however, because not every object may be mentally
solved. Thus, draftsmen often use projection theory to help them derive
and check surfaces about which they are unsure. Let us assume, for
example, that surface 1-2-3-4 in Figure 5-2 has caused confusion and
that we have numbered what we feel are the correct three views. We
now wish to check our work.

To check the proposed solution, start with point 1 and draw in
the projection rectangle verifying the indicated locations of point 1. Do
the same with line 1-2 and then with surface 1-2-3-4. All points, lines,
and the plane check. Therefore, the drawn solution is correct.

Figure 5-3 is another example of an object containing all normal
surfaces.

Three Views of an Object

Chap. 5

Figure 5-3 An object and a three view orthographic drawing of
that object.

5-3 HIDDEN LINES

Most objects contain lines (edges) that cannot be seen in all three
views. The slot in Figure 5-4 appears in the top and right side view, but
it is hidden in the front view. We must somehow represent the slot in
the front view to insure that all views are consistent in the information
they present. We do this by using hidden lines.

Hidden lines are lines used to represent edges of an ob-
ject that cannot be directly seen.

Axiom 5-2

Figure 5-4 An example of an object whose front view contains
a hidden line.

Sec. 5-3

Hidden Lines

The hidden lines in the front view of the object shown in Figure 5-4
represent the horizontal surface of the slot.

Hidden lines are drawn by using dashes as explained in Figure 5-5.
The actual length of the dashes may vary according to the situation as
long as a 4 to 1 ratio is maintained between the dashes and the inter-
mittent spaces. Since hidden lines are not as dark or as thick as object
lines, you should be careful to make sure that there is a noticeable dif-
ference between object lines and hidden lines. See Chapter 2 for further
definition of kinds of lines.

There are three rules that must be followed when drawing hidden
lines. They have been developed to prevent confusion and misunder-
standing in the use and interpretation of hidden lines. Figure 5-6 il-
lustrates the rules.

hW-4

Figure 5-5 Hidden line configuration.

Rule 1: Do not continue an object line into a hidden
line. Always allow a small (1/16) gap.

Axiom 5-3

Figure 5-6(a) Do not continue a visible line into a hidden line;
leave a gap.

Rule 2: Show hidden corners as an intersection of hid-
den lines, thereby specifically defining the location of

the corner.

Axiom 5-4

Figure 5-6(b) Show hidden intersections by crossed hidden lines.

Rule 3: Never draw parallel hidden lines with equal
length dashes and spaces. Stagger the lengths so that
each line is distinctive. Axiom 5-5

figures 5-7, 5-8, 5-9, and 5-10 are further examples of hidden FitfUM R R , M «_„„ f . . . .

lino nmWoma rlgure 5-6(c) Stagger the spacing of clow

ime problems. parallel hidden lines.

Figure 5-7 An example of an object whose orthographic views
contain hidden lines.

rui

Figure 5-8 An example of an object whose orthographic views
contain hidden lines.

Figure 5-9 An example of an object whose orthographic views
contain hidden lines.

Figure 5-10 An example of an object whose orthographic views
contain hidden lines.

Three Views of an Object

Chap. 5

5-4 INCLINED SURFACES

Figure 5-11 shows an object that has an inclined surface 1-2-3-4.
An inclined surface is one that is parallel to one, but not both, principal
plane lines. Note that the top and right side views are approximately
the same as those shown for the example in Figure 5-1 and note the
incline of plane 1-2-3-4 may only be seen in the front view. This kind
of visual ambiguity is unavoidable in orthographic views, and as shown
here it emphasizes the importance of using all orthographic views to-
gether to form a final solution to the problem.

Figures 5-12 and 5-13 are other sample problems which include
inclined surfaces.

Figure 5-11 An object with an inclined surface 1-2-3-4.

Figure 5-12 An object with an inclined surface.

Sec. 5-5

Curved Surfaces

Figure 5-13 An object with inclined surfaces.

5-5 CURVED SURFACES

Figure 5-14 shows an object that has a curved surface. A curved
surface is one that appears as a part of a circle (an arc of constant radius)
in one of the orthographic views. Curved surfaces are similar to slanted
surfaces in that they tend to generate ambiguous orthographic views.

A unique characteristic of curved surfaces is the tangency line.
Surface 1-2-3-4 in Figure 5-14 contains a tangency line 5-6 repre-
sented by a phantom line, A tangency line represents the location at
which the round portion of surface 1-2-3-4 flairs into (becomes tan-
gent to) the flat horizontal portion. Because there is no edge here, a

Figure 5-14 An object with a curved surface.

13 5,6

1.5

2,4

Three Views of an Object

Chap. 5

line would not be drawn in any of the views. Figure 5-15 shows an
object in which the curved surface does form an edge with the lines
labeled 7-8 and 9-10; thus, it requires an object line. Without excep-
tion, you may always draw an visible line when the round surface forms
an edge with the other surfaces.

You cannot, however, always omit a line if a physical edge does
not appear. Figure 5-16 gives two examples of objects that require lines
in their orthographic views even though no edges actually exist on the
object. Figure 5-17 is another example of an object that does not re-
quire a line.

r~ r

f++

Figure 5-15 An object with a curved surface.
Figure 5-16 Two objects with curved surfaces.

I j

Sec. 5-6

Sketching

! ■
i

l
1

i
i
i

f ^M

Figure 5-17 An object with curved surfaces.

As a rule, if a curve changes direction (goes from concave to con-
vex, or vice versa) such that any part of it becomes parallel to one of
the principal plane lines, a line is required.

5-6 SKETCHING

Before a draftsman begins the actual drawing of a new assignment
he will usually make a sketch of the object involved. He then studies
the sketch and tries to identify any problems that could arise when he
makes his drawing. If any problems are found, he reworks his sketch
until the problems are solved and his sketch has become a clear well-
understood picture of his future drawing. A draftsman takes the time
to create good sketches because it is much easier to correct freehand
sketches than to correct finished drawings. The time he spends sketch-
ing is more than regained when he creates his drawing because he avoids
the problems he found and corrected while he was making his sketches

Of course, learning to sketch is easier for those who have artistic
ability, but anyone can learn to sketch. The following hints are offered
to make it easier for you to learn to sketch:

To make sketches of orthographic views (see Figure 5-18):

SOLUTION:

1. Use grid paper, graph paper, quadrapads, and so on. This kind
of paper will help you to establish an approximate scale and
thereby keep your sketches fairly proportioned. It will also
help you to keep your lines straight.

GIVEN: An object.

PROBLEM: Sketch the front, top and
right side views.

Figure 5-1 8(a)

Three Views of an Object

Chap. S

2. Lightly sketch the overall shape of the object, as would be seen
in the three basic orthographic views.

: :

— >H ' j

L _l_ -1

- 1 . T M
i

:: " : +=E:E t :=::i:~
EEE::--::±:=::::

Figure 5-1 8(b)

3. Lightly sketch in the specific details of the object.

■ [TrH || [j 1 1 -111

_ ■ —

| j 1 1 -li

1 I 1 1 1 i \\ II -UN

; Z

Figure 5-18(c)

Sec. 5-6

Sketching

4. When the desired shape is completed, darken in the important
lines by using heavy, bold strokes.

. 7T"~^ .

. _ . .

-i _ i

l ~"

" :

n *

? ""

(<i

""" _

. h

i u

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Figure 5-1 8(d)

To make a picture (isometric) sketch (see Figure 5-19):

GIVEN: Three views of an object.

PROBLEM : Sketch an isometric picture of the object.

-0" "0-

ttt
I I I

J-U

TTT

I I I
111

Figure 5-19(a)

100

Three Views of an Object

Chap. 5

SOLUTION:

1. Draw a block whose length, width, and height are of approxi-
mately the same proportions as those of the object to be
sketched. Make the receding lines of the box 30°.

Figure 5-19(b)

2. Lightly sketch in the specific details of the object.

Figure 5-19(c)

Figure 5-19(d)

3. When the desired shape is completed, darken in the important
lines by using heavy, bold strokes.

Figure 5-19(e)

Sec. 5-7

Visualization Techniques

101

5-7 VISUALIZATION TECHNIQUES

Visualizing an object in three dimensions, given only the ortho-
graphic views, has always been a problem for draftsmen. Drawing
and sketching experience and good depth perception help, but there
are always those problems that just "can't be seen." Two techniques
used by draftsmen to help visualize difficult problems are model build-
ing and surface coloring.

Models offer the best visualization aids because they themselves
are three-dimensional objects, but models are usually expensive and
time-consuming to build. Figure 5-20 shows examples of some well-
constructed models. To overcome the expense and time constraints,
some draftsmen make models out of children's modeling clay. Figure
5-20 shows an example. Clay models are not meant to be exact-scaled
duplications, but rather approximate representations made to help a
draftsman visualize the object being drawn; thus, the quality of clay
models may vary according to personal requirements and situations.

Figure 5-20 Models used to help visualize. The model in the
center is made from children's modeling clay,

Figure 5-21 shows an example of surface coloring. Draftsmen
generally color by using different colors {red, blue, etc.), but the example
in Figure 5-21 was done by using various shades of gray. By coloring a
surface with the same color in all the different views, the surface may
be more easily identified in the various views and therefore more easily
visualized.

102

Three Views of an Object

Chap. 5

__ 1 1

Figure 5-21 An example of surface shading.

PROBLEMS

Draw or sketch, as assigned by your instructor, three views (front, top,
and right side) of the following objects. Each triangle in the grid pattern
is 0.20 on a side, except for problems 5-1 and 5-3 which-use a 0.25 on
a side grid pattern.

5-2

Pro b ferns

5-7

5-8

104

Three Views of an Object

Chap. 5

5-9

5-10

1.00

5-11

5-12

75-2 PLACES

Problems

105

5-13

5-14

1.00 R

1.00 DIA

1.00

1.00R

5-15

106

5-16

Three Views of an Object

Chap. 5

.50R- 3 PLACES

.50DIA-4 PLACES

. - --

5-17

5-18

1.00

2.00 R
3.00 DIA

.50DIA

5-19

2.63

Problems

107

5-20

1.50DIA

5-21

5-22

5-23

Top

108

Three Views of an Object

Chap. 5

In the following, redraw the two given views and add the thud as re-
quired. If assigned, prepare a freehand three-dimensional sketch of the
object. Each square on the grid pattern is 0.20 per side.

If"

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5-24

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Problems

109

5-26 Problem created by Steve Gertz.

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69DIA

2.00 —
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.25

.50

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5-28 Dimensions are in millimeters.
— 60 -

FRONT 20m *

110

5-29

Three Views of an Object

Chap. 5

4PLACES-25DIA
.38R

1.00

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-J- 2024-T4AL

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ALL INSIDE BEND RADII ^

DIMENSIONS
AND TOLERANCES

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Figure 6-0 Illustration courtesy of Teledyne Post, Des Plaines,
Illinois 60016.

6-1 INTRODUCTION

This chapter explains and illustrates dimensioning and tolerancing.
The picture portion of a drawing defines the shape of the object; the
dimensions define the size; and the tolerances define the amount of
variance permitted in the size. All three pieces of information are
needed to form a clear, understandable, manufacturable drawing.

To help you gain an understanding of the relationships between
size, shape, and tolerance, look at Figure 6-1. What is the height of
the car? Is it full size or is it merely a model? We may get some ap-
proximation of the height by comparing the height of the car with the
height of the girl. If we use the girl for our scale, we may say that
the car is a little less than one-half a girl height. Here the picture gives
us shape and the girl gives us an approximate size— but what about the
tolerance? How tall is the girl? Is she wearing high-heeled shoes or is
she standing on a box? For a more accurate answer, we need a more
accurate scale.

Figure 6-1 How high is the car? Photograph courtesy of General
Motors Corp.

112

Sec. 6-2 Extension Lines, Dimension Lines, Leader Lines, and Arrowheads

113

The post beside the girl has been calibrated into 6 inches-intervals.
Further, it has been cut off and labeled 35V6 inches. If the post is our
scale and the 35V& inches-label is our dimension, we are assured of a
more accurate measurement. As before, since the accuracy of our final
measurement depends on the accuracy of our scale, we would pick a
scale that satisfies our specific tolerance requirement. If we just want
to know about how high the car is, the girl would be sufficient. If we
want to know within an inch, the post dimension would probably be
acceptable. If we want a more accurate answer, we would have to use
a more accurate scale.

As you read through this chapter, remember that dimensions are
the most important part of any drawing. Always try to dimension your
drawings clearly, concisely, and in an easily understandable manner.

6-2 EXTENSION LINES, DIMENSION
LINES, LEADER LINES,
AND ARROWHEADS

Dimensions are placed on a drawing by using a system of exten-
sion lines, dimension lines, leader lines, and arrowheads. Figure 6-2
illustrates how these various kinds of lines are used for dimensioning.
The lines are defined as follows:

EXTENSION LINES: used to indicate the extension of an edge or

point to a location outside the part outline. *

DIMENSION LINES: show the direction and extent of a dimension. *

LEADER LINES: used to direct an expression, in note form, to the

intended place on the drawing. The leader line should terminate in an

arrowhead or dot. *

ARROWHEADS: used to indicate the ends of dimension lines and the

ends of some leader lines. * Arrowheads are drawn as shown in Figure

6-3.

Figure 6-2 Extension, dimension and leader lines.

♦Extractec from American Drafting Standards; Line Conventions, Sectioning,
and Lettering (ASA Y14-2-1957) with the permission of the publisher, The Ameri-
can Society of Mechanical Engineers, 29 West 39 St., New York, N.Y.

114

Dimensions and Tolerances

Chap. 6

•°r,

r*et

*»o<*

>H«o^

Figure 6-3 Arrowheads.

6-3 LOCATING AND PRESENTING
DIMENSIONS

How do you locate and present dimensions on a drawing so that
they may be easily and unmistakably understood? Unfortunately; there
is no one answer to this question. Each drawing must be dimensioned
according to its individual requirements, and what is acceptable in one
situation may not be acceptable in another situation. Learning how to
locate and how to present dimensions depends a great deal on drawing
experience, but there are some general guidelines that may be followed.
These guidelines are presented below and are illustrated in Figure 6-4.
6-4(a). Dimension by using extension, dimension, and leader
lines placed neatly around the various views of the ob-
ject. Place dimensions so that your reader will have no
difficulty understanding which surface or which edge
you are defining.

1,00-

2.38

1.75

1.00

-.38

Figure 6-4(a)

Sec. 6-3

Locating and Presenting Dimensions

IIS

6-4(b). Be sure that the size of the object is completely defined
and that no surfaces or edges are left out.

.50 Oi A

*o^xo*

2.00

1.00

.SOW A

Figure 6-4(b)

6 -4(c). Always keep dimensions at one constant height. 1/8 or
3/16 is the generally accepted height, although a larger
height may be used in some cases (title blocks, page num-
bers, and so on). Letters and numbers should never be
less than 1/8 in height.

2.00

1.25

Figure 6-4(c)

116

Dimensions and Tolerances

Chap. 6

6-4(d). Do not squeeze dimensions into small spaces and angles.
Undersized dimensions are difficult to read.

Figure 6-4(d)

6-4(e). Unless it is absolutely necessary, do not put any dimen-
sions within the visible lines of the object being defined.
You will never know when or how a drawing may have to
be changed. It is important that you realize that drawing
changes are not necessarily the result of errors. Customer
requirements may change, designs may be modified, a
new machine may be added to your company's manufac-
turing process, and so on. Any one of these reasons, and
many more, could necessitate drawing changes.

-i 1,88— *-

Figure 6-4(e)

Sec. 6-3

Locating and Presenting Dimensions

117

6-4(f). Do not overdimension. Too many dimensions are as con-
fusing as too few dimensions. A common mistake is to
double dimension, that is, to dimension the same dis-
tance twice on the same drawing. One dimension per
distance is sufficient.

Figure 6-4(f )

6-4(g). Do not place dimensions too close to the object tp be de-
fined. A dimension line should never be closer than 3/8
to the object.

Figure 6-4(g)

118

Dimensions and Tolerances

Chap. 6

6-4(h). Leader lines should all be at the same angle. This will tend
to give the drawing a more organized appearance.

75DIA

.50DIA

1.00 Dl A

1.00 DIA

Figure 6 -4(h)

6-4(i). Space dimensions evenly. This not only gives the drawing
a well-organized appearance, but it also makes the dimen-
sions much easier to read.

Figure 6-4(i)

Sec. 6-3

Locating and Presenting Dimensions

119

6-4(j). Leader lines should not change directions until after they
have extended beyond the outside edge of the object and
beyond any dimension or extension lines. Leader lines
should always end in a short horizontal section that will
guide the reader's eye into the appropriate note.

-88DIA

tso

—75

-«-i-*^

! *-

Figure 6-4(j)

6-4(k). Use either decimals or fractions. Do not mix the two.
Some companies make exception to this by having criti-
cal dimensions written in decimal form and noncritical
dimensions written in fractional form. No such variance
is in effect for the problems in this book.

t.38

2.00

.50

.63

Figure 6-4(k)

120

Dimensions and Tolerances

Chap. 6

6-4(1). Use either the unidirectional or aligned system. Do not
mix the two.

100

Figure 6-4(1)

6-4(m). Unless it is absolutely necessary, do not dimension to a
hidden line. In most cases, the addition of a section cut
(see Chapter 13) to the drawing is probably the best way
to eliminate excess or confusing hidden lines.

1.00

*■ ^

r— - 1

1,00

Figure 6-4(m)

Sec. 6-3

Locating and Presenting Dimensions

121

6-4(n). Do not include the symbol for inches (") on dimensions.
All dimensions in mechanical drafting are in inches unless
otherwise stated. An exception to this rule is the number
1 which is usually written 1" so it will not make vertical
dimensions lines appear as center lines.

Figure 6-4(n)

6-4(o). Always specify whether or not a hole or arc dimension is
a diameter or a radius. Usually, holes are dimensioned in
diameters (DIA) and arcs are dimensioned by radii (R).

,63

Figure 6-4(o)

122

Dimensions and Tolerances

Chap. 6

-.75

1.00

6-4(p). Do not run extension or dimension lines through other
dimension or extension lines unless there is absolutely no
other alternative. The same is true for leader lirieti.

.62

t
2.00

i.aa

I l :

5-^

-62

■*■ 1.38 ■*■
-< 2.0<

Figure 6-4(p)

6-4(q). Always include overall dimensions except dtr objects that
have rounded ends. This means the total length, width,
and height for rectangular objects and the largest outside
diameter and height for cylinders.

2.00

IjOO

2.00

1.00

Figure 6-4(q)

6-4(r). Always dimension holes in the views in which they ap-
pear as circles.

1.25 01 A

Figure 6-4(r)

Sec. 6-5

Dimensioning Holes

123

64 UNIDIRECTIONAL AND
ALIGNED SYSTEMS

Dimensions may be positioned on a drawing by using either the
unidirectional or the aligned system. The unidirectional system is the
preferred system. In the unidirectional system, all dimensions are
placed so that they may be read from the bottom of the drawing, that
is, with their guidelines horizontal. In the aligned system, dimensions
are placed so that they may be read from either the bottom or the
right side of the drawing, that is, with their guidelines parallel to the
surface that they are defining. Figure 6-5 illustrates the difference
between the two systems.

The unidirectional system is the newer of the two systems and it
has become the most popular because it is easier to draw and to read.
All problems in this book are dimensioned by using the unidirectional
system.

Unidirectional

Aligned

Figure 6-5 A comparison between the unidirectional and aliened
dimensioning system.

6-5 DIMENSIONING HOLES

Figure 6-6 illustrates several different ways to dimension holes.
Holes are usually dimensioned to their diameters because most drills,
punches, and boring machines are set up in terms of diameters. Arcs
are usually dimensioned according to their radii.

Always locate a hole by dimensioning to its center point. Make
sure that the center point of the hole is clearly defined by crossing
the short sections of center lines. The long sections of the center lines
may be dimensioned as if they were extension lines.

When you use leader lines, always point the arrow end of the
line at the center point of the hole. Always finish the non-arrow end

Figure 6-6 Different ways to dimension holes and arcs.

with a short horizontal section that will guide the reader's eye into the
dimension note. Always place dimension notes so that they may be
read from the bottom of the drawing.

6-6 DIMENSIONING ANGLES
AND HOLES

Figure 6-7 illustrates several different ways to dimension angles.
It also illustrates the angular (dimensioned with angles) and the coordi-
nate (dimensioned using the center lines as base lines) systems of
dimensioning holes on an object.

Figure 6-7 Examples of angle and hole dimensioning.

124

Sec. 6-8

Base Line System

125

6-7 DIMENSIONING SMALL DISTANCES
AND SMALL ANGLES

When you dimension a small distance or a small angle, always
keep the lettering at the normal height of either 1/8 or 3/16. The
temptation is to squeeze the dimensions into the smaller space. This
is unacceptable because crowded or cramped dimensions are difficult
to read, especially on blueprints which are microfilmed. Figure 6-8
shows several different ways to dimension small distances or angles
and still keep the dimensions at the normal height.

25 u

3.00

H h-,25

.64

-.36

H*h

Figure 6-8 Different ways to dimension small distances and
angles.

6-8 BASE LINE SYSTEM

The base line system of dimensioning is illustrated in Figure 6-9.
All dimensions in the same plane are located from the same line which
is called a base line. (It is sometimes called a reference line or a datum
line.) This system is particularly useful because it eliminates tolerance

Figure 6-9 Baseline system.

Baselines

1.13 Dl A

126

Dimensions and Tolerances

Chap. 6

buildup, it is easy for manufacturers and inspectors to follow, and it
is easily adaptable to the requirements of numerical tape machines.
Its chief disadvantage is that the amount of space used on the drawing
paper is larger— usually at least twice the area of the surface being de-
fined. Also, once it is set up, it is difficult to alter.

When you use the base line system, be careful to include all needed
dimensions and be sure to use a large enough piece of paper.

6-9 HOLE-TO-HOLE SYSTEM

The hole-to-hole system is illustrated in Figure 6-10. It is a modi-
fication of the base line system (Section 6-8) which is used to dimen-
sion parts whose hole-to-hole distances are critical, for example, a part
that must align with the shafts or dowels of another part for proper
assembly.

In the hole-to-hole system, all dimensions in the same plane are
measured for the lines that define the critical holes. The base line is
not, in this case, a physical line, but it is the center line between the
critical holes.

38DIA-4 PLACES

-50R -4 PLACES

Figure 6-10 Hole-to-hole system.

6-10 COORDINATE SYSTEM

The coordinate system is a dimensioning system based on the
mathematical x-y coordinate system. It is usually only used to dimen-
sion an object that contains a great many holes, for example, an electrical
chassis. It is particularly well-suited to computer use and numerically
controlled tape machines.

Each hole on the given surface is located relative to an x-y coordi-
nate system and then all values are listed in a chart. The overall dimen-
sions are not included in the chart but are located on the picture part
of the drawing. Figure 6-11 is an example of an object dimensioned by
using the coordinate system.

6-11 TABULAR DIMENSIONS

Often manufacturers will produce a part in several different sizes.
Each part will have the same basic shape, but the part will vary in over-

Sec. 6-11

Tabular Dimensions

127

3jOO

HOLE

DIA

0,50

0.50

.470

1.50

0.50

.470

2.50

0.50

470

0.88

1.62

.375

2.00

1.38

375

0.38

2.62

.250

2.25

.625

Figure 6-11 Coordinate system.

all size. To save having to dimension each part individually, a system
called tabular dimensioning is used. Figure 6-12 illustrates an example
of tabular dimensioning.

To read tabular dimensions, look up the part number in the table
and substitute the given numerical values for the appropriate letters in
the figure. For example, part number 1003, according to the table, has
an A value of 2.25, a B value of 1.50, and so on. Part number 1005
has an A value of 2.50, a R value of 1.75, and so on. The numerical
dimensions of .50 mean that these dimensions do not vary, that they
remain the same for all parts.

The table may also be used in reverse. If you know what your
given design requirements are, look up these values in the table to find
which part number you should call out on the drawing.

.50

— A *-

' .50

+ 1

PART NO

1001

2.00

1.38

.50

1,00

1002

2,00

1.38

.50

.68

1.13

1003

2.25

1.50

.68

.75

1.13

1004

2.25

1.50

.ao

.75

1.25

1005

2.38

1.75

.68

.75

1.25

C DIA

Figure 6-12 Tabular dimensions.

Sec. 6-11

Tabular Dimensions

127

3jOO

HOLE

DIA

0.50

.470

1.50

050

.470

2.50

0.50

.470

0.88

1.62

.375

2j00

1.38

375

0.38

2.62

.250

2.25

.625

Figure 6-11 Coordinate system.

all size. To save having to dimension each part individually, a system
called tabular dimensioning is used. Figure 6-12 illustrates an example
of tabular dimensioning.

To read tabular dimensions, look up the part number in the table
and substitute the given numerical values for the appropriate letters in
the figure. For example, part number 1003, according to the table, has
an A value of 2.25, a B value of 1.50, and so on. Part number 1005
has an A value of 2.50, a B value of 1.75, and so on. The numerical
dimensions of .50 mean that these dimensions do not vary, that they
remain the same for all parts.

The table may also be used in reverse. If you know what your
given design requirements are, look up these values in the table to find
which part number you should call out on the drawing.

PART MO

1001

2.00

138

.66

.50

1.00

1002

2.00

1.38

.50

.68

1.13

1 003

2.25

1.50

.68

.75

1.13

1004

2.25

1.50

.75

1.25

1005

2.38

1-75

.68

.75

1.25

C DIA

Figure 6-12 Tabular dimensions.

128

Dimensions and Tolerances

Chap^6

6-12 IRREGULARLY SHAPED CURVES

To dimension an irregularly shaped curve, dimension the points
that define the line. The more points you dimension, the more accurate
will be your definition. Figure 6-13 illustrates a dimensioned irregularly
shaped curve.

2.00

Figure 6-13 Dimensioning an irregular
curve.

Figure 6-14 Some common dimensioning
errors.

.25DIA

Figure 6-15 The errors illustrated in
Figure 6-14 corrected.

COMMON DIMENSIONING ERRORS

Figure 6-14 demonstrates some of the most common dimensioning
errors. Note how cluttered and confined the dimensions appear. Com-
pare Figure 6-14 with Figure 6-15. Both drawings are of the same
shape, but Figure 6-15 is dimensioned properly.

Study the errors in Figure 6-14 and then see how they were cor-
rected in Figure 6-15. The errors are:

(a). No arrowhead

(b). Dimension line too thick

(c). No gap between object and extension line

(d). Dimension value placed over a center line

(e). No gap between dimension line and dimension value

(f). Arrowhead extends beyond extension line

(g). Leader line changes direction within the object

(h). Dimension value written too close to the object and over a

dimension line
(i). Fraction used while all other dimensions are in decimal form
(j). Extension line too long
(k). Dimension not written horizontally.

6-14 TOLERANCES

No dimension can be made perfectly. Unless you are very lucky,
there will always be some variance. If, for example, you call for a di-
mension to be made 5 inches long, you will not get exactly 5 inches on
the finished part. It may measure 5.0001 or 4.99999, etc., but it will
not be exactly 5 inches.

It is not only impossible to manufacture perfect dimensions, it is
also unnecessary. It is possible for a carpenter to build a house within
the nearest 0.01 inches, but it isn't necessary for the structural sound-

Sec. 6-15

Cumulative Tolerances

129

ness of the house. Think of how much time such a constraint would
add to the normal time required to build a house, and then think of
how this extra time would needlessly affect the building cost of the
house.

Because it is impossible to manufacture perfect dimensions, all
dimensions must be toleranced. Each dimension must be considered
separately in regard to how much variance is acceptable to insure a
satisfactory finished product. The final judgment must be made by
considering, among other things, manufacturing capabilities, customer
requirements, usage requirements, material properties, and cost con-
straints. It takes experience and practice to make such a judgment cor-
rectly.

Many companies have "standard" tolerances. That is, their shops
will always work to a given standard tolerance unless they are specifical-
ly told to do otherwise. The standard tolerance is usually printed on the
drawing as part of the company's title block.

Figure 6-16 is a sample of standard tolerance. The notation x.xx ±
0.01 means that any dimension that has two decimal places must be
manufactured within 0.01 of the stated value. For example, a dimen-
sion of 2.04 may be manufactured as small as 2.03 or as large as 2.05
and still be an acceptable part. The other notations in the block are
interpreted in a similar manner.

Tolerances — Unless

Otherw

ise

Specified are:

Two Place

Deci

mals

(.XX) ±

.010

Three Place

> Decimals

(.XXX) ±

.003

Angular ±1°

Figure 6-16 A standard tolerance notation.

Figure 6-17 illustrates several different ways that a tolerance may
be specified on a drawing. Each notation is a different way of telling
the builder the limits that he must work within.

There are many different kinds of tolerances; each one has its own
notations and symbols. For example, surface tolerances y/ ', roundness
tolerances O, squareness tolerances 1, and so on. To cover them all is
beyond the scope of this book because each represents a very specialized
field of study.

6-15 CUMULATIVE TOLERANCES

Cumulative tolerances are errors that occur when several small,
seemingly insignificant errors are compounded. Usually, they are the
result of improper dimensioning, For example, consider Figure 6-18(a),
and assume that the object is being manufactured to a standard compa-

,500 ±.001 oi A

30°±2°

2.01

Figure 6-17 Different ways to specify
tolerances on a drawing.

130

Dimensions and Tolerances

Chap. 6

(b)

-4) — <fe — ©-

«— 1.00 -H

* 2.00

4.00

-i

©— <JH

too

(c)

[- — 1.00 ■*•

3.00

4O0 —
4.00 —

<+— 1.00 -*■

1.00

(d)

r-<— 1.00
Figure 6-18 Cumulative tolerances.

4.00
REF

-4) — & — ©-

•1J0O-*

1.00

-*- 1.00-

ny tolerance of ±0.02 for all two-placed dimensions. Each of the 1.00
dimensions could be made 1.02 giving an overall length of 4.08.

1.02
1.02
1.02
1.02
4.08

4 08 is not an acceptable overall length, since the overall length must
be according to the given dimension, 4.00 ± 0.02. This means that the
greatest acceptable length is 4.02. The 4.08 object would not pass
inspection. Unfortunately, the responsibility for this error must be
placed directly on the draftsman who improperly dimensioned the ob-

There are several other ways to avoid the error in Figure 6-18(a).
In Figure 6-18(b), a REF note (reference note) was placed on the 4.00
dimension The REF notation means that the dimension is not critical
to the manufacturing of the object and has only been included for the
reader's convenience. Be very careful when you use the REF notation
that it is only used for insignificant dimensions.

In Figure 6-18(c) one of the 1.00 dimensions was dropped, inis
means that the end section of the object, which is now not dimen-

Problems

131

sioned, may vary. All the other dimensions are still manufactured
within stated tolerances. In Figure 6-1 8(d) the base line system of
dimensioning was used. In most cases, the base line system is the best
way to avoid cumulative tolerances because no one dimension is de-
pendent on the accuracy of another dimension. Each dimension is
manufactured separately.

PROBLEMS

Redraw and dimension the following shapes and objects. Each square
on the grid pattern is Va per side.

6-1

6-2

6-3

6-4

6-5

-— — , — „ — . , , i

-ULLI I 1 I I I I I I I 1 M I I I I I I I I I I 1 I I I I I -

132

6-6

Dimensions and Tolerances

Chap. 6

—

Redraw and dimension the following shapes. Each square on the grid
pattern is .20 per side.

6-7

—

6-8

6-9

' XX -1- I f 1 I 1 1 I

~ x x - 4- I- — '

^ i

/"' ™2 t £

f~ r - \

z Z \ ^

.A -A \c ^

L. L- 5

J — — — — L

— '

_. — ■

------

- " ~ ~ -

~ : . .

Problems

133

6-10

6-11

6-12

6-13

xrtrr

!s;

6-14

6-15

§;

r---s

$=:*

134

Dimensions and Tolerances

Chap. 6

6-16

6-17

;

SEAtl

6-18 Dimension the following chassis surface twice; once using the
base line system and once using the coordinate system.

e=:s

S==2

Draw three views of the following objects and dimensions. Use both the
decimal and the unidirectional system. Each triangle or square on the
grid pattern is .20 per side.

6-19

Problems

135

6-20

6-21

6-22

6-24

i _^_„__ r ::

^> ^

— . _

— ^^

K.y

r ^„ \ UdZ

L V^ ±.U

6-23 -j-

„_ m. — 1

-£^

b i

136

Dimensions and Tolerances

Chap. 6

6-25 What is the maximum and minimum height that the following
five pieces could generate if their dimensions and tolerances are
as follows:

(a) 1.38 ± 0.06

(b, 0.63 ♦_ 0-00

, v ! Kn + 0.02

(d) 1.000 ± 0.004

(e) 1-3/8 ± 1/32

Max

? ?

Min

6-26 In the following problem, all linear dimensions have a tolerance
of ± 0.03 and all angular dimensions have a tolerance of ± 1°. If
the disc piece is placed within the 90° -opening of the larger base
piece, what is the maximum height that the two pieces together
could generate? Prepare a layout to verify your answer.

Problems

137

6-27 Redraw the following object and insert the following dimensions:

„ _ 9 7 = + 0.01

a -z.it) _ 0Q2

b = 1.88 ± 0.01
c = 1.130 ± 0.002
d = 2.38 ± 0.01

« = 2 000 + ° 003
e z.uuu _ Q 0Q2

f - 1 q«p + o.oo

f - 1.38iH _ Q Q1

i? = 2 00 + ° 05
* z,uu - 0.00

ft = 30° ± 5°

i = 0.750 ± 0.001

j = 1.25 ± 0.03

6-28 Dimension the following object by using the tabular system. For
part number

1001: V 1 = 3.00, V 9 = 1.80, V, = 2.00, V A = .80

1002: V 1 = 3.20, V, = 1.90, Fg = 2.00, V 4 = .80

1003: V x = 4.00, V^ = 2.20, V> = 2.20, V 4 = .80

1004: V a = 4.00, V 2 = 2.20, Vg = 2.40, V 4 = 1.00

v 4

t)r

:=*

~-i

-,t

Each square on the grid pattern is 0.20 per side.

OBLIQUE SURFACES

AND EDGES

Figure 7-0 Photograph courtesy of General Motors Corp.

7-1 INTRODUCTION

Oblique surfaces and edges are made up of planes and lines that are
not parallel to either principal plane line. Figure 7-1 is an example of an
oblique surface. Note that none of the lines that define the surface is
parallel to either principal plane line and that each line is a different
length in each given orthographic view. Note also that the shape of the
plane also varies in each orthographic view. This variance makes it
difficult to visualize what oblique surfaces really look like (what is
their true shape) and will force you to rely on projection theory to
help you to formulate accurate finished drawings.

This chapter explains and illustrates the kinds of oblique surfaces
most often found in drawings.

7-2 COMPOUND EDGES AND LINES

Figure 7-2 is a problem that involves a compound edge. The prob-
lem is to draw the top view, given the front and right side views. Figure
7-3 is the solution and was derived by the following procedure:

Figure 7-1 An oblique surface.

GIVEN: Front and side views.
PROBLEM: Draw the top view.

Figure 7-2

139

140

Oblique Surfaces and Edges

Chap. 7

SOLUTION:

1. Make, to the best of your ability, a freehand sketch of the solu-
tion and, if possible, an isometric sketch of the entire object.

Figure 7 -8(a)

2. Analyze the given information and label those points about
which you are unsure. In this example surfaces 1-2-3-4 and
3-4-5-6 were labeled.

4.5

1.4.

3.6

2.3

Figure 7 -3(b)

Sec. 7-2

Compound Edges and Lines

141

3. Project points 1, 2, 3, 4, 5, and 6 into the top view by using the
projection theory presented in Chapter 4.

Figure 7 -3(c)

4. Using very light construction lines, lay out the top view of sur-
faces 1-2-3-4 and 3-4-5-6. Also lightly lay out the remainder
of the object.

Figure 7-3(d)

142

Oblique Surfaces and Edges

Chap. 7

5. Erase all excess lines and darken in all the lines to their final
color and configuration.

Figure 7-3(e)

GIVEN: An object.

PROBLEM: Draw a front, top, and side

views.

Figure 7-4

SOLUTION:

In this example line 3-4 is a compound edge. It was formed by the
intersection of two inclined surfaces; yet line 3-4 is not parallel to
either principal plane line.

Figure 7-4 is another problem that involves a compound edge. In
this problem the object is pictured (an isometric drawing is presented)
and you are asked to draw all three orthographic views: front, top, and
right side. Figure 7-5 is the solution and was derived by the following
procedure:

1. Make, to the best of your ability, a sketch of the solution.
-Make the sketches as complete and as accurate as you can. It is
much easier to change sketches than to change drawings.

Figure 7-5(a)

Sec. 7-2

Compound Edges and Lines

143

Working from your sketches, lightly lay out the solution. If
necessary, label any confusing areas and use projection theory
to work known pieces of information together to formulate
the final solution. Alsoi use projection theory to check any
areas about which you are unsure.

Figure 7-5(b)

3. When the layout is complete, erase all excess lines and draw in
all lines to their final color and configuration.

4^ 4>

-•I.I

Figure 7-5(c)

144

Oblique Surfaces and Edges

Chap, 7

7-3 OBLIQUE SURFACES

Figure 7-6 is a problem that involves an oblique surface. An
oblique surface is one that is not parallel to either principal plane line
(see Figure 6-1). The problem is to draw the front view given the top

GIVEN: Top and side views.
PROBLEMS: Draw front view

Figure 7-6

and right side views. Figure 7-7 is the solution and was derived by the
following procedure:

1. Make, to the best of your ability, a freehand sketch of the solu-
tion and, if possible, an isometric sketch of the entire object.

SOLUTION:

Sec. 7-3

Oblique Cuts

145

2. Analyze the given information and label those points, lines, or
planes about which you are unsure. In this example surface
1-2-3-4 was labeled.

Figure 7-7<b)

3. Project points 1, 2, 3, and 4 into the front view by using pro-
jection theory.

Figure 7-7(c)

146

Oblique Surfaces and Edges

Chap. 7

4. Using very light layout lines, lay out the front view of surface
1-2-3-4. Also lay out the remainder of the object.

Figure 7 -7(d)

5. Erase all excess lines and draw in all lines to their final color
and configuration.

Figure 7 -7(e)

Surface 1-2-3-4 in Figure 7-7 is an oblique surface. It is not paral-
lel to either of the principal plane lines. Because it is not parallel to
either principal plane line, none of the three final views represents a
true picture of the shape of surface 1-2-3-4. How to find the true
shape of an oblique surface is explained in Section 11-6.

Sec. 7-4

Parallel Edges

147

Figure 7-8 is another example of a problem involving an oblique
surface.

Scale ^-=1
4

GIVEN: An object.

PROBLEM: Draw front, top, and side

views.

Figure 7-8 Three views of an object which contains oblique sur-
faces.

7-4 PARALLEL EDGES

Figure 7-9 is an example of a problem that involves parallel edges.
Parallel edges are edges that are parallel to each other and may or may
not be parallel to the principal plane lines. The problem is to draw the
front, top, and right side view when an isometric drawing is given.
Figure 7-10 is the solution and was derived by using the same proce-
dure outlined for Figure 7-6.

SOLUTION:

Figure 7-10(a)

Figure 7-9

148

Oblique Surfaces and Edges

Chap. 7

Figure 7 -10(b)

Figure 7-10(c)

In this problem surface 1-2-3-4-5-6-7-8 is an oblique flat surface
that cuts across the object. The' object was (before it was cut by sur-
face 1-2-3-4-5-6-7-8) shaped l&e a backward C and it is important to
realize that the object is still basically shaped like a backward C. (Note
the left side view.) The fact that the object contains an oblique surface
that cuts through several other surfaces need not complicate the draw-
ing of orthographic views. Look back at Section 7-3 which illustrated
and explained how to draw oblique surfaces and compare the solution
to Figure 7-6 with the solution to Figure 7-9. With the exception of
the horizontal slot in Figure 7-9, the problems are the same.

Figure 7-11 is another example of a problem that involves parallel
edges.

Sec. 7-5

Dihedral Angles

149

Scale; ^ = 1
4

J=J

Figure 7-11 Three views of an object which contains several sets
of parallel edges.

7-5 DIHEDRAL ANGLES

Figure 7-12 is a problem that involves a dihedral angle. A dihedral
angle is an angle between two planes. The problem is to draw the front
view of the object when the top and right side views are given. Figure
7-13 is the solution and was derived by the procedure on the following
page:

GIVEN: Top and side views.
PROBLEM: Draw front view.

Figure 7-12

150

Oblique Surfaces and Edges

Chap. 7

SOLUTION:

1. Make, to the best of your ability, a freehand sketch of the solu-
tion and, if possible, a sketch of the entire object.

Figure 7 -13(a)

2. Define the vortex line of the dihedral angle. In this example the
vortex line is defined as line 1-2.

4 2 5

3 I

Figure 7-1 3(b)

Sec. 7-5

Dihedral Angles

151

3. Define the surfaces that make up the dihedral angle. In this
problem the surfaces are 3-4-1-2 and 1-2-5-6.

4 2 s

¥■

4,5

Figure 7-1 3(c)

4. Project points 1,2,3,4,5, and 6 into the front view by using
projection theory.

Z 5

3,6

4£

Figure 7 -13(d)

152

Oblique Surfaces and Edges

Chap. 7

5. Using very light lines, lay out the front view of surfaces 3-4-1-2
and 1-2-5-6. After checking your work, complete the initial
layout of the entire object.

Figure 7-1 3(e)

6. Erase all excess lines and darken in all lines to their final color
and configuration.

Figure 7-14 is another example of a problem that involves a di-
hedral angle.

Scale: 3 =1

Figure 7-14 Three views of an object which contains several dia-
hedral angles.

Sec. 7-6 Holes In Oblique Surfaces 153

7-6 HOLES IN OBLIQUE SURFACES

Figure 7-15 is a problem that involves a hole in an oblique surface.
The problem is to draw the top view of the object when the front and
right side views are given. Figure 7-16 is the solution and was derived
by the following procedure:

GIVEN: Front and side views.
PROBLEM: Draw top view.

SOLUTION:

1. Make, to the best of your ability, a sketch of the solution and,
if possible, the entire object.

Figure 7-16(a)

154

Oblique Surfaces and Edges

Chap. 7

2. Using very light lines, draw the top view (not including the
hole) by using the procedure outlined for oblique surfaces in
Section 7-3.

-7

/ **

v 4

T T"V

K-

2 \

Figure 7 -16(b)

3. In the right side view, where the hole appears as a circle, mark
off and label points 5 through 16 at 30° -intervals around the
circle. Although these points do not really exist on the circle,
they are to be used for reference.

rJiU

^/\L/\to

\ ^-"Tv^ /11

16V7

\7l2

1b 14

-13

Figure 7 -16(c)

Sec. 7-6

Holes In Oblique Surfaces

155

Project points 5 through 16 from the right side view into the
front view as shown in Figure 7-16. Label the points. Be care-
ful not to reverse the points when you project between views.
For example, points 16 and 12 are on the same horizontal
projection line, but point 16 is to the left of center and point
12 is to the right of center.

Figure 7-1 6(d)

5. Using the information from the front and right side views,
project points 5 through 16 into the top view. Check each
point carefully.

Figure 7 -16(e)

1S6

Oblique Surfaces and Edges

Chap. 7

6. Erase all excess lines and darken in all lines to their final color
and configuration.

GIVEN: An object.

PROBLEM: Draw front, top, and side

views.

Figure 7-16(f)

Figure 7-17

The use of 30° -intervals in step 3 was made simply because it is
easy to draw 30°-angles with a T-square and a 30-60-90 triangle as a
guide. Any angle could have been used, including randomly spaced
angles. The more points used, the more accurate will be the projected
ellipse.

But what if we must work from an isometric drawing? Figure 7-17
shows an isometric drawing of the object used for Figure 7-15, but this
time we know less about the shape of the hole because we are given
much less information to work with. Nevertheless, we can draw three
views -of the object, including the hole. Figure 7-18 is the drawing
sequence used to convert the isometric drawing given in Figure 7-17 to
three orthographic views. The following procedure was used:

SOLUTION:

1. Draw the front, top, and side views of the object from the
given information. You will not be able to include the hole.

Sec. 7-6

Holes In Oblique Surfaces

157

2. Since we know that the hole will be drilled in a horizontal
direction and that it will be centered in the object, we can
draw it as a circle in the right side view.

Figure,7-18(b)

3. Using a T-square and 30-60-90 triangle, mark off lines,
30° apart, in the right side view as shown. Label the lines.

Figure 7-18(c)

158

Oblique Surfaces and Edges

Chap. 7

4. Project lines A-I, L-K, and J-B into the front view by pro-
jecting points A, L, and J from line 4-1 in the side view to
line 4_i in the front view and points I, K, and B from line
3-2 in the side to line 3-2 in the front view. Note that lines
A-I, L-K, and J-B cannot be projected into the top view and
that lines C-D, E-F, and C-H cannot be projected into the
front view.

Figure 7 -18(d)

5. Project points A, L, J, I, K, and B from the front view to the
top view as shown.

Figure 7 -18(e)

Sec. 7-6

Holes In Oblique Surfaces

159

6. Project points C, E, G, H, F, and D from the top view into the
front view as shown.

Figure 7-18(f)

7. Draw in lines A-B, C-D, E-F, G-H, I-J, and L-K in the front
and top views.

1 H F D2 1 H F D2

Figure 7-18(g)

160

Oblique Surfaces and Edges

Chap. 7

8. In the side view, label the intersections that the 30°-lines
make with the side view of the hole.

3 1KB ?

4 A L J 1

4CEG3

1HFD2

C £ G 3

r / T4

K Jn "

H F D

Figure 7 -18(h)

9. Project points 6, 7, 8, 9, 10, 12, 13, 14, 15, and 16 into the
front view and points 9, 10, 11, 12, 13, 15, 16, 5, 6, and 7
into the top view. Note that points 5 and 11 cannot be pro-
jected into the front view and that points 8 and 14 cannot be
projected into the top view.

Figure 7-1 8(i)

Sec. 7-6

Holes In Oblique Surfaces

161

10. Project points 8 and 14 from the front view to the top view
and project points 5 and 11 from the top view to the front
view.

Figure 7-18(j)

11. The hole is now defined in each view. Erase all excess lines
and darken in the final lines (including the hole) to their prop-
er color and configuration.

Figure 7-18(k)

162

Oblique Surfaces and Edges

Chap. 7

7-7 INTERNAL SURFACES IN
OBLIQUE SURFACES

Figure 7-19 is a problem that involves an internal surface in an
oblique surface. This kind of problem is very similar to problems that
involve holes in oblique surfaces. The problem here is to draw the front
view of the object when the top and right side views are given. Figure
7-20 is the solution and was derived by the listed procedure:

GIVEN: Top and side views.
PROBLEM: Draw front view.

Figure 7-19

SOLUTION:

1. Draw a front view of the object. Include the oblique surface
and omit the internal surfaces. Use the outline presented in
Section 7-3.

Figure 7 -20(a)

Sec. 7-7

Internal Surfaces In Oblique Surfaces

163

3. 2

4 1

Figure 7-20(b)

2. .Number the points of the internal surfaces in the given views.
In this example the six corners of the hexagon cutout were
labeled points 5, 6, 7, 8, 9, and 10.

3 2

4 1

Figure 7 -20(c)

164

Oblique Surfaces and Edges

Chap. 7

3- Using projection theory, project points 5 through 10 into
the front view.

Figure 7-20(d )

4. Erase all excess lines and darken in all lines to their final color
and configuration.

Figure 7 -20(e)

When you work on a problem that involves internal surfaces, it is
important that you carefully label the intersection of the internal sur-
faces with the outer surfaces. If necessary, add imaginary points (as
was dpne for holes in internal surfaces) to help insure an accurate pro-
jection of the shape of the intersection.

Problems
PROBLEMS

Draw three views (front, top, and side) of the following objects:
7-1

7-3

1.13

3.13

2.38

7-2

HEXAGON
1.75 ACBOSS FLATS

-50X.50 SQUARE HOLE
Perpendicular to
inclined surface

LSG

166

Oblique Surfaces and Edges

Chap. 7

7-5

2 LARGE HOLE3-.75DIA
1 SMALL HOLE -.50 DIA

.75

20 R

Millemetera

For each of the following problems, redraw the given two views and
add the appropriate view so that each object is defined by a front, top,
and side view. Each square of the grid pattern is 0.20 on each side.

7-7

;94R

30*\

2.36

■60°

Problems

167

7-8

===5^=2====

::: :-::::::_s-:=:::::=:::::-:
—j-r 1— : s ~j -

7-9

■

,o0

-* 2.00 *i

,31^- t.38-H

-.50

45 <L-

-* 2.00-

.25

7-10

7-11

1.75
.25-

"ZEL

ao°— Ay/ U- 1

1-38

—.33

1.08

7-12

168

Oblique Surfaces and Edges

Chap. 7

7-13

7-14 This problem is based on information supplied courtesy of Wendt-
Sonis/Unimet Division of TRW, Inc.

2.00

7-15

»..

■-J

-s

,94 R

7-16

Problems

7-17 Problem courtesy of Mr. Tony Lazaris,

169

2.sa

4.00

.38— H h— — M U— .38

CYLINDERS

Figure 8-0 Photograph courtesy of Detroit Diesel Allison, Divi-
sion of General Motors Corp.

8-1 INTRODUCTION

Cylinder problems are problems whose basic geometric shape is a
cylinder. They are often difficult to visualize and draw because they have
no natural flat surfaces, making it confusing to know where to start. Fig-
ure 8-1 demonstrates this point by showing front, top, and right side
views of a natural, uncut cylinder. The front and top views are identical
and regardless of how the cylinder is rotated about the center point, x,
the front and top views remain identical. How can we label or reference
cylinders to make sure that those who read the finished drawings clear-
ly understand which view is the front and which is the top?

The key to solving the problems is in using the center lines. The
right side view of Figure 8-1 defines vertical and horizontal center
lines which divide the cylinder into four equal quadrants. Where the
horizontal and vertical center lines cross the periphery of the cylinder
is defined as center line edge points, and are marked points 1, 2, 3, 4,
5, 6, 7, and 8. They are all double points and represent the end views
of longitudinal center lines which can be seen in the front and top
views. These longitudinal center lines 1-2, 3-4, 5-6, and 7-8 can be
used to define the cylinder's height and width and can be used as the-
oretical base lines from which to reference variances from the basic
cylindrical shape (cuts, chamfers, and so on).

It should be understood that although longitudinal center lines
do not physically exist on cylindrical pieces, they represent where the
curved surface of the cylinder changes direction (see Section 5-5).

Center lines will be used throughout this chapter, as they are in
industry, to define and give reference to cylinder problems. The first
step in any cylinder problem should be to define the center lines.

6
4

Figure 8-1 Three views of a cylinder.

171

172 Cylinders

8-2 CUTS ABOVE THE CENTER LINE

Chap. 8

Figure 8-2 is an example of a cylinder cut lengthwise above the
center line. The problem is to find the top view when the front and
right side views are given. Figure 8-3 is the solution and was derived
by the following procedure:

GIVEN: Front and side views.
PROBLEM: Draw top view.

Figure 8-2 Cylinder cut above the centerline.

SOLUTION:

1. Define the horizontal center line edge points— 5, 6, 7, and 8— in
the front and right side views.

3.4

Figure 8-3(a)

Sec. 8-2

Cuts Above the Center Line

173

2. Project points 5, 6, 7, and 8 into the top view; then, using
construction lines, connect the points to form a rectangle.

3. Define the cut surface 1, 2, 3, and 4 in the front and right side
views.

3 2

4 1

3.4 12

5,6

5S/

\67

Figure 8-3(b)

4. Project points 1, 2, 3, and 4 into the top view and, using con-
struction lines, connect the points to form a rectangle.

5. Darken in the two rectangles with object lines.

Figure 8-3(c)

Although a technical solution to the problem has been derived,
there still may be some difficulty in visualizing what it means. The cut
surface 1-2-3-4 which appears as a rectangle in the top view, appears as
a straight line in both the front and right side views. The surfaces 8-5-
1-4 and 3-2-6-7 appear in the top view to be similar to the flat surface

174

Cylinders

Chap. 8

l_2-3-4, but they are not. Surfaces 8-5-1-4 and 3-2-6-7 are curved
surfaces that start at horizontal center lines 5-8 and 7-6 and extend up-
ward to lines 4-1 and 7-6. Study the right side view to verify the length,
height, and shape of the curve. Remember that although center edge
lines 8-5 and 7-6 do not really appear on the piece, they represent the
widest part of the cylinder and where the curve defining the periphery
changes directions from outward to inward (see Section 4-7).

8-3 CUTS BELOW THE CENTER LINE

Figure 8-4 is an example of a cylinder cut lengthwise below the
center line. The problem is to find the top view when the front and side

GIVEN: Front and side views.
PROBLEM: Draw the top view.

Figure 8-4 Cylinders cut below the centerline.

views are given. Figure 8-5 is the solution and was derived by the fol-
lowing procedure:

SOLUTION:

1. Define the four comers of the cut surface 1-2-3-4 in the front
and top views.

Figure 8-5(a)

Sec. 8-3 Cuts Below the Center Line

2. Project points 1, 2, 3, and 4 into the top view.

175

4 2

3 1

£Z

J ' 4 |

1,2

Figure 8 -5(b)

3, Connect points 1, 2, 3, and 4 with object lines to complete
the top view.

Figure 8-5(c)

The plane 1-2-3-4 is a flat surface that has around surf ace directly
under it.

176 Inclined Cuts Chap. 8

8-4 INCLINED CUTS

Figure 8-6 is an example of an inclined cut. The problem is to find
the top view when the front and right side views are given. Figure 8-7
is the solution and was derived by the listed procedure:

GIVEN: Front and side view.
PROBLEM: Draw top view.

Figure 8-6 Cylinder with an inclined cut.
SOLUTION:

1. Define the horizontal center line edge points 1, 9, 10, and 11 in
the front and right side views.

2. Project the horizontal center line edge points 1, 9, 10, and 11
into the top view thereby defining the outside edge of the cyl-
inder.

3. Create points 2, 3, 4, 5, 6, 7, and 8 in the right side view by
marking off angles of 0°, 30°, 60°, 90°, 60°, 30°, and 0° from
the horizontal center line (30° -increments were chosen because
they are easy to draw with a 30-60-90 triangle). These points
are for drawing purposes only and do not represent any corners
or edges which appear on the piece and, therefore, they should
be drawn very lightly. Once the solution has been derived, these
points should be erased.

4. Project points 2, 3, 4, 5, 6, 7, and 8 into the front view. This is
done by drawing lines parallel to the horizontal principal plane
line from the created points 2, 3, 4, 5, 6, 7, and 8 to the in-
clined surface in the front view. Points (6, 4), (7, 3), and (8, 2)
become double points in the front view.

5. Project points 2, 3, 4, 5, 6, 7, and 8 into the top view.

6. Using a French curve, carefully draw in the elliptical shape by
connecting points 2, 3, 4, 5, 6, 7, and 8. Be careful to avoid a
lumpy or ragged curve. The finished ellipse should be smooth
and symmetrical.

7. Complete the top view by projecting the necessary points from
the front and right side views.

10,11

Figure 8-7(a)

? n

8,4*

v"?

\t J

10,11

8,2

J 39

1,9

Figure 8-7(b)

Figure 8-7(c)

177

178

8-5 CURVED CUTS

Cylinders

Chap. 8

Figure 8-8 is an example of a cylinder with a curved cut. The prob-
lem is to find the top view when the front and right side views are given.
Figure 8-9 is the solution and was derived by the listed procedure:

GIVEN: Front and side views.
PROBLEM: Draw the top view.

Figure 8-8 Cylinder with a curved cut.

SOLUTION:

1. Define the horizontal center line edge points 1, 2, 3, and 4 in
the front and right side views.

Figure 8-9(a)

Sec. 8-5

Curved Cuts

179

2. Project the horizontal center line edge points 1, 2, 3, and 4 into
the top view thereby defining the outside edge of the cylinder.

Figure 8-9(b)

3. Create points 5, 6, 7, 8, 9, 10, and 11 in the right side view by
• marking off angles of 0°, 30°, 60°, 90°, 60°, 30°, and 0° from
the horizontal center line (30° increments were chosen because
they are easy to draw with a 30-60-90 triangle). These points
are for drawing purposes only and would never appear on the
piece; therefore, they should be drawn very lightly. After the
solution has been derived, these points should be erased.

Figure 8-9(c)

180

Cylinders

Chap. 8

4. Project points 5, 6, 7, 8, 9, 10, and 11 into the front view. This
is done by drawing lines parallel to the horizontal principal
plane line from the created points 5, 6, 7, 8, 9, 10, and 11 to
the inclined surface in the front view. Points (5, 11), (6, 10),
and (7, 9) become double points in the front view.

Figure 8-9(d)

5. Project points 5, 6, 7, 8, 9, 10, and 11 into the top view.

— A>-*"

3 /

7 * 9 1

(

1,4

6,10-

2,3 34 (

5,11

Figure 8-9(e)

Sec. 8-6

Chamfers

181

6. Using a French curve, carefully draw in the elliptical shape by
connecting points 5, 6, 7, 8, 9, 10, and 11. Be careful to avoid
a lumpy or ragged curve. The finished ellipse should be smooth
and symmetrical.

Figure 8-9(f )

7. Complete the top view by projecting necessary points from the
front and right side views.

This~ procedure is exactly the same as that used in Section 8-4 to
solve inclined cut problems. However, because of the difference in the
kind of cut, the resulting ellipse in the top view is different.

8-6 CHAMFERS

Chamfers are machine cuts, usually at 45°, along the edges or cor-
ners of machined pieces. They are used to eliminate sharp, dangerous
edges, to trim off material for clearance requirements, or to act as a
kind of taper in aligning parts. They are not unique to cylinder prob-
lems and Figure 8-10 gives two examples of chamfers in noncylindrical
pieces. Figure 8-11 is an example of cylindrical chamfers. The problem
is to find the top view where the front and right side views are given.
Only the chamfered sections are labeled since the rest of the solution
has been previously explained (Section 8-1).

Consider line 2-3-4-5 in the right side view of Figure 8-12. It is
an end view of a flat plane that was developed by machining away part
of the cylinder and then chamfering the end. The chamfer creates two
edge lines that show as concentric circles in the right side view and as
parallel lines in the front view. This means that points 3 and 4 are in
front of points 2 and 5 and that lines 2-3 and 4-5 are slanted in the top
view. After defining points 2, 3, 4, and 5 in the front and side views,
project them into the top view and draw lines 2-3, 3-4, and 4-5. There
is no line 2-5. Why?

182

Cylinders

Chap. 8

J-x45°CHAMFER

-J-x45°CHAMFER

Figure 8-10 Chamfers on non-cylindrical shaped objects.

GIVEN: Front and side views.
PROBLEM: Draw the top-view.

P ~w>

Figure 8-11 Cylinder with chamfers.

SOLUTION:

1& 2534

Figure 8-1 2(a)

16 23

Figure 8-1 2(b)

Figure 8-1 2(c)

P "^

183

184

Cylinders

Chap. 8

8-7 HOLES

When holes are drilled in cylinders, holes create unique drawing
and projection problems. Figure 8-13 is an example of a cylinder that
has two holes drilled completely through from top to bottom. Detail A
is an enlargement of the top surface and has been drawn twice scale to
accent the elliptical shape generated by the round hole. Even at twice
scale, the ellipse is almost flat. Thus, in most drawings the ellipse is
neglected and is drawn as a straight line as shown in Figure 8-13. This
irregularity is acceptable drafting practice since it does not affect the
accuracy of the communication. A machinist needs only to know what
size hole and where to put it, and the fact that a round drill generates
a slight elliptical shape in an orthographic projection will not affect his
method of drilling. The ellipse is an unimportant result of the drilling
and may be omitted.

DETAIL A

-|-DIA-2PLACES

SEE DETAIL A

Draw as a straight line

Figure 8-13 How to draw holes in cylinders.

This is not true if the hole is large. Where is the crossover point?
When does a hole become large enough to require an ellipse to be drawn?
There is no fixed rule to follow and the draftsman must use his own dis-
cretion depending on his particular situation.

8-8 ECCENTRIC CYLINDERS

Eccentric cylinders are two or more cylinders whose center points
are not matched. One cylinder is off center in relation to the other.
Some students feel that eccentric problems are created by instructors
who are eccentric, but no research has been done to prove or, for that
matter, disprove this theory.

Sec. 8-8

Eccentric Cylinders

185

Eccentric problems should be approached as separate and indepen-
dent cylinder problems. Break down the problems into the sections that
make them up and solve them separately; then rejoin them to form a
composite solution. Figure 8-14 is an example of an eccentric cylinder
problem that requires a top view when front and right side views are
given. Figure 8-15 is the solution and was derived by the listed pro-
cedure:

GIVEN: Front and side views.
PROBLEM: Draw the front view.

Figure 8-14 Eccentric cylinders.

SOLUTION:

1. Define the center line edge points 1, 2, 3, and 4 of the smaller
diameter cylinder in the front and right side views.

2. Project points 1, 2, 3, and 4 into the top view.

1.2

Figure 8-1 5(a)

186

Cylinders

Chap. 8

3. Define the center line edge points 5, 6, 7, and 8 of the larger
diameter cylinder in the front and right side views.

5,71

3,4

5,6

\s.8

1.2

1 ' 3 Vv

Figure 8-1 5(b)

4. Project points 5, 6, 7, and 8 into the top view.

Figure 8-1 5(c)

5. Draw in the appropriate visible lines.

8-9 HOLLOW SECTIONS

Figure 8-16 is an example of a hollow cylinder. The problem is
to find the top view when the front and right side views are given.
Figure 8-17 is the solution and was arrived at by considering the out-
side and inside diameters as separate cylinders, solving them inde-
pendently, and forming a composite solution. The following steps were
used:

Sec. 8-9

Hollow Sections

187

GIVEN: Front and side views.
PROBLEM: Draw top view.

Figure 8-16 Hollow cylinders.

SOLUTION:

On the outside cylinder, define the horizontal center line edge
points of the cut surface 1-2-7-8 in the front and right side
views. In other words, consider the problem to consist only of
a solid cylinder, cut directly on the horizontal center line (see
Section 8-2).

1.357

246 8

Figure 8-1 7(a)

2. Repeat step 1 for the inside cylinder, defining points 3, 4, 5,
and 6.

Igj Cylinders Chap. 8

3. Project points 1, 2, 3, 4, 5, 6, 7, and 8 into the top view.

Figure 8-1 7(b)

4. Draw in the surfaces 1-2-3-4 and 5-6-7-8. Note that surfaces
1-2-6-5 and 3-4-6-7 are flat rectangles and, with the excep-
tion of the cylinder's ends, are the only flat surfaces in the
problems.

5. Complete the top view by projecting necessary points from the
front and right side views.

Figure 8-17(c)

Problems

189

PROBLEMS

Draw three views (front, top, and right side) of the following objects.
If two views are given, redraw the given views and add the missing third
view. Make a freehand three-dimensional sketch of the object if requested
by your instructor. If a three-dimensional picture is used to present the
object, draw the front, top, and right side views. Each square on the
grid pattern is 0.20 per side.

8-1

3,50

-1.13

2.25 DIA

8-2

8-3

3.00

1.50

190

8-4

8-5

Cylinders

Chap. 8

4.00

3.00 *-

2.00

1.00

•—.25 TYP

2.00 01 A

8-6

i-7

Problems

191

8-8

1.00-

2.13

■*- 1.50

■« *

8-9

->-

8-10

192

8-11

Cylinders

Chap. 8

«3

:*s

8-12

.75 R

1.50 DIA

8-13 All dimensions are in millimeters.

58 DIA

14 DIA

Problems

193

8-14

8-16

150 DIA

1.38DIA

8-15

1,75 DIA

1.13

8-17 Use B-size paper (11 X 17).

2,75 DIA

CASTINGS

Figure 9-0 A five-range MT 650 automatic transmission being
pressure tested. Photograph courtesy of Detroit Diesel Allison— a
Division of General Motors Corp.

9-1 INTRODUCTION

Objects which are made using the casting process present unique
drawing problems. Because edges of cast objects are not square (90°),
they cannot appear as lines in orthographic views. Also, these nonsquare
edges often intersect each other which results in many unusually shaped
lines. This chapter will present the techniques used to draw cast objects
and will show how rounded edges may be represented.

9-2 FILLETS AND ROUNDS

A fillet is a concaved-shaped edge. A round is a convex shaped edge.
Figure 9-1 illustrates these definitions. The size of a fillet or round is
usually specified on a drawing by a note such as:

ALL FILLETS AND ROUNDS -^R

although they may be dimensioned individually.

From a drawing standpoint, fillets and rounds only appear in views
taken at 90° to them, as shown in Figure 9-2. Note in Figure 9-2 that
the lines that seem to represent edges represent surfaces. The actual
edges are rounded and so do not appear in orthographic views unless
they are shown in profile.

Round

Fillet

-Round

Figure 9-1 Fillets and rounds.

^**-

ALL FILLETS & ROUNDS -J-R

Figure 9-2 Orthographic views of a cast object.

196

Castings

Chap. 9

Most fillets and rounds are drawn by using a circle template be-
cause they are too small to be easily drawn with a compass. Remember
that when you use a circle template the hole sizes are given in diameters,
not radii. Therefore, be sure to convert the given fillet and round sizes
to diameters before you draw them.

9-3 ROUND EDGE REPRESENTATION

When you draw cast objects, how do you properly represent round-
ed edges? Should the small curved lines, as shown in Figure 9-3(a) be
used? Should the long, phantom lines, as shown in Figure 9-3(b),
be used? Or should no lines be used, as shown in Figure 9-3(c)?

In general, the small curved lines and the phantom lines are only
used to indicate a rounded edge in a pictorial drawing. They are not
used in orthographic views. However, since representation practices
vary from company to company, always check the company standards
before you start a drawing.

Figure 9-3 No special shading or line work is required to repre-
sent the rounded edges of cast object.

( "i 1

J •>

(c)

Sec. 9-4 Runouts 197

94 RUNOUTS

A runout is the intersection of two or more rounded edges. Run-
outs appear on a drawing as curved sections at the end of the lines that
represent surfaces. They generally turn out (that is, away from the sur-
face lines), but this is not a hard, fast rule. Elliptical surfaces generate
runouts that turn in ? as illustrated in Figure 9-4. Each object must be
judged individually as to which runout direction looks the most realistic.

Figure 9-5 shows several different examples of runouts. Draw run-
outs either freehand or by using a curve as a guide.

Runout

Figure 9-4 A drawing which includes a
runout.

/&\

4 i

J I j

I 1 '

I
> ) \ *

Figure 9-5 Example of two objects whose orthographic views in-
clude runouts.

198 Castings

9-5 SPOTFACES AND BOSSES

Chap. 9

Spotfacing is a special machining operation that smoothes out the
otherwise rough surface finish found on cast objects. It is similar to
counterboring, but during spotfacing the surface of the object is cut
just deep enough to produce a machined quality finish.

Spotfacing is called out on a drawing by a note as shown in Figure
9-6. First, the drill diameter is given, then the drill depth, if any, and

aV?%°

*o°*o<

.500 DRILL — 1.000 S FACE

Boss

Spotface

Drawn ^

Figure 9-6 A drawing which includes a spotface and a boss.

finally the diameter of the spotface. Spotface depth is not specified un-
less it is a design requirement. The machinist will cut just deep enough
into the object to smooth out the surface.

When you draw a spotface, draw the spotface depth 1/16". This
depth enables the drawing reader to clearly see the spotface and is con-
venient to draw. Other parts of the note are interpreted as shown in
Figure 9-6.

A boss is a raised portion of a casting as shown in Figure 9-6.
Bosses are usually added to castings because they can be easily machined
(being higher than the rest of the cast surface). Bosses are usually as
high as the given fillet and round size.

9-6 MACHINING MARKS

Machining marks are used to differentiate those surfaces on a
casting which are to be machined. Figure 9-7 illustrates different ma-
chining marks and shows how they are used.

Problems

199

ft.

Rough

Coarse

Medium

Fine

V = Very fine

r- About -|-

60 v TVP Both sides

Figure 9-7 Machining marks are used to indicate the quality of
the surface finish required.

PROBLEMS

Draw three views (front, top, and side) of each of the following objects:

9-1

All fillets and rounds =J^R

.75DIA

.50 Dl
4 PLAC

38DIA-2 PLACES

.38 REF

200

9-2

Castings

Chap. 9

75DIA

1.38

9-3

All fillets and rounds = -g-R

DIA-2 PLACES

69
i31DIA-4 PLACES

Problems

201

For the following problems, redraw the two given views and add the
required missing view. Each square on the grid pattern is 0.20 per side.

9-4

TOP

All fillets and rounds = ^R

-— 1,50— ■-

C~ "^

3.00

.50

-« *-

LOO

r >

\
I 1M

■

-* 2.00 *

"75

9-5

202

9-6

Castings

Chap. 9

TOP

All fillets and rounds =4-R

1,25 Ol A

1.75

-1,25
-.25

■1.13

9-7

:3jI

^-^i£_«LtU^- HILSJ^lC^

~ /

£ — r-^ 7 r ~* — 5 1** Z ~ r ~I

* — *< -- Z L

h/->=>^ 2 t-

12 11^ t I -

ti ti i

J ^ 1 _ 1 '- - *^' k. J f *

■7*"* H l ^i**!* J > IP jj ~

r " " "

Problems

203

9-8

TOP

All fillets and rounds = |-R

9-9

;

I5> _

1 _. , _ , —

»* -^, — ^.- ^ — _^— , *r*-> 1

j + r^ -- V

::::::::^:2: == -5-"~r::::::;::::r-;;:: = z:::

. _ . — ^^^___

..-_ „ i . — .

SECTIONAL VIEWS

Figure 10-0 A model 400 Turbo Hydramatic. Photograph cour-
tesy of General Motors Corp.

10-1 INTRODUCTION

Sectional views are used to expose internal surfaces of an object
that would otherwise be hidden from direct view. Sectional views
greatly add to the clarity of a drawing because they do not contain
any hidden lines.

To help you understand the differences between section cuts and
regular orthographic views, study Figures 10-1 and 10-2. In Figure
10-1 note the clarity of the internal profile of the object shown in the
sectional view. In Figure 10-2 note that the sectional views are much
easier to understand than are the regular orthographic views which
contain many hidden lines. This does not mean that sectional views
should be used instead of regular orthographic views. Sometimes sec-

t i0

1^°

SECTION A-A

Figure 10-1 A comparison between a regular orthographic view
and a sectional view.

205

206

Sectional Views

Chap. 10

t-;+
i i

...J-

^TTl^

\\M

V T^

z-Trri

**£*•

*® v >r

Figure 10-2 A comparison between regular orthographic views
and sectional views.

tional views may be used to replace confusing regular orthographic
views. At other times both views may be used. There are also many
drawings that would not require section cuts at all. When and where
to use a sectional view depends on the object being drawn. However, in
any. situation, your prime concern should be that your drawings are
easily understood. Always be as clear and direct as possible in the views
that you present.

10-2 CUTTING PLANE LINES

Cutting plane lines are used to define the line along which an ob-
ject is to be cut. They are drawn by using either of the two configura-
tions shown in Figure 10-3. They should be drawn by using very heavy
and very black lines— as heavy and black, if not more so, than visible
lines.

Cutting plane lines need not go directly through an object but may
be offset as shown in Figures 10-4 and 10-5. Cutting plane lines are
offset so that several internal surfaces may be shown in the same sec-
tional view. The fact that a cutting plane line is offset does not appear
in the sectional view. There should be no lines in the sectional view to
indicate that the cutting plane line has changed direction.

The arrowheads of a cutting plane line indicate the direction in
which to observe the sectional view. The actual section view should be

Sec. 1 0-2

Cutting Plane Lines

207

L_-

3 * < 1
f to 1 T

16
Figure 10-3 Cutting plane line configurations.

Figure 10-4 An offset cutting plane line.

Figure 10-5 An offset cutting plane line.

located behind the arrowheads or, if absolutely necessary, in alignment
with the cutting plane line as illustrated in Figure 10-6. Under no cir-
cumstances should the sectional view be placed ahead of the cutting
plane line arrowheads.

To help you visualize this convention, think of yourself as standing
on the sectional view looking at the object being drawn. The cutting
plane line arrowheads should point in the direction in which you are
looking—away from the sectional view.

208

Sectional Views

Chap. 10

«**° 3SS

ssfr

Figure 10-6 Sectional view locations relative to the cutting plane
line.

10-3 SECTION LINES

Section lines are used to indicate where, in a sectional view, solid
material has been cut. There are many different section line patterns (a
different pattern for each building material), but the most common pat-
tern is the one shown in Figure 10-7. The lines are thin and black
(about one-half as thick as visible lines) and are drawn at any inclined
angle (45° is most often used).

When two or more parts are gut by the same cutting plane line, the
section cut lines must be varied to indicate clearly the different parts.
Section lines may be drawn at different angles or with different spacing
as is illustrated in Figure 10-8.

Any Inclinded Angle
(Usually 45°)

Any Uniform Spacing
J= Of Greater

(Usually^-)

Figure 10-7 Section lines.

Figure 10-8 Four different objects in the
same sectional view.

Sec. 10-3

Section Lines

209

Incorrect

G°*

Figure 10-9 The correct alignment of section lines.

Do not draw section lines so that they are parallel to any surface
in the object. For example, the upper right corner of the object pic-
tured in Figure 10-9 is a 45° surface. It is wrong to draw section lines
at 45°, parallel to the 45° surface. The lines must be drawn at another
angle so that they are not parallel to the 45° surface.

There are several techniques draftsmen use to draw section lines.
One is to use an Ames Lettering Guide. Another is to slip a piece of
graph paper under the drawing, align it as desired, and then trace the
lines. Another technique is to scribe a line onto a 45-45-90 triangle
as shown in Figure 10-10. Scribe the guide line 1/8" from and parallel
to the edge of the triangle. If desired, several lines may be scribed.

Figure 10-10 A 45-45-90 triangle which has a line scribed along
the longest edge (see arrow). This scribed line is parallel to and
1/8 from the edge of the triangle. Use the scribed line to align
the triangle when drawing section lines.

SECTION B-B
SECTION A-A SECTION C-C

Figure 10-11 Multiple sectional views.

10-4 MULTIPLE SECTIONAL VIEWS

It is possible \p take many sectional views through the same ortho-
graphic view. Figure 10-11 demonstrates this by showing three sec-
tional views, each taken through a different position of the same top
view. Note how each sectional view is placed behind the arrowheads of
the cutting plane line. As many sectional views as are necessary for clear
definition of the object being studied may be shown.

Although hidden lines are not shown in sectional views, visible
lines are shown. Note, for example, that the V formation located on the
back left surface of the object appears in all three sectional views. Any
surface that may be directly seen, even if it is not located directly on
the path of the cutting plane line, must be shown. For example, the tall
center portion of the object shown in Figure 10-12 appears in section

Same Edge

SECTION B-B

SECTION A-A

Figure 10-12 Multiple sectional views.

210

Sec. 10-6

Half Sectional Views

211

A-A because it may be directly seen. The shorter end section cannot be
directly seen and, therefore, is not shown. However, note that part of
the shorter left end section may be directly seen through the hole and,
because it may be seen, it must be shown in the sectional view. Since in
section B-B we are beyond the tall center section, it will be omitted in
the sectional view.

10-5 REVOLVED SECTIONAL VIEWS

It is sometimes possible to save drawing a separate sectional view
by drawing a sectional view directly on the regular orthographic view.
This sectional view is called a revolved sectional view and is illustrated
in Figure 10-13. A revolved sectional view is used to define the shape
of an object that has a constant shape.

Figure 10-13 Revolved sectional views.

Figure 10-14 illustrates another revolved sectional view. This time
the object has been broken open and the revolved sectional view has
been placed between break lines. Either revolved sectional view (Figure
10-13 or Figure 10-14) is acceptable.

EZZZZZ22ZZZ3

Figure 10-14 A revolved sectional view.

10-6 HALF SECTIONAL VIEWS

Regular orthographic views and sectional views may be combined
within the same orthographic view to form a half sectional view. Figure
10-1 5(a) shows a half sectional view. Note that the two views are
separated by a center line and that each half is drawn independently of
the other. The regular orthographic part of the view shows hidden lines,
but the sectional view part does not. Half sections are particularly use-
ful for drawing symmetrical objects.

Study the cutting plane line in Figure 10- 15(a) and note how the
left arrowhead is placed directly on the center line. Compare this with
the cutting plane line of Figure 10-1 5(b) and then compare the dif-
ferences in the resultant sectional views. By drawing the cutting plane
line as shown in Figure 10-15(b), we eliminate the need to draw all
hidden lines on the left side of the sectional view. Both Figures 10-
15(a) and 10-15(b) are acceptable ways of drawing half sectional views.

212

Sectional Views

Chap. 10

Figure 10-1 5(a) A half sectional view.

Figure 10-1 5(b) A half sectional view..

10-7 BROKEN OUT SECTIONAL VIEWS

Sometimes less than a full or half sectional view is sufficient to
clarify some internal surfaces of an object. In Figure 10-16, for example,
the internal surfaces are symmetrical both vertically and horizontally.
That is, the left and right halves are exactly the same as the top and
bottom halves. Therefore, in this example we only need to show a
small piece of the internal surfaces to give the reader a good idea of
the entire internal shape of the object. We do this by using a broken
out sectional view as shown in Figure 10-16.

Figure 10-16 A broken out sectional view.

Broken out sectional views are sectional views drawn on a regular
orthographic view and are created by theoretically breaking off a part
of the external surface of the object, thereby exposing some of the
internal surfaces to direct view. When you break open the object, use
a break line to outline the place where the external surfaces have been
broken. A cutting plane line is not required.

Figure 10-17 is another example of a broken out sectional view.

Sec. 10-8

Projection Theory

213

Figure 10-17 A broken out sectional view.

10-8 PROJECTION THEORY

The projection theory presented in Chapter 4 and continued
throughout this book is also applicable to sectional views. Figure 10-18
illustrates its application.

Most sectional views are drawn without the aid of projection theory,
but as with regular orthographic views, projection theory is very helpful
in checking lines.

A -♦-'a -* J

SECT C-C

SECT B-B

SECT A-A

Figure 10-18 A multiple sectional view problem solved using
projection theory.

214

Sectional Views

Chap. 10

10-9 HOLES IN SECTIONAL VIEWS

A common mistake that is made in drawing holes in a sectional
view is to omit the back edge of the hole. Even if a hole is cut in half
in a sectional view, the back edges must be shown in the sectional view.
Figure 10-19, which shows a counterbored hole, uses an isometric
drawing, a regular orthographic view, and a sectional view. In each view
the arrows point to approximately the same point on the back edge of
the hole. Note how lines that represent the back edges of the hole ap-
pear in the sectional view. When you draw holes in a sectional view,
make sure that the back edge of the hole is represented.

Back Edge of Hole

Figure 10-19 A hole in a sectional view.

10-10 AUXILIARY SECTIONAL VIEWS

Auxiliary sectional views may be created in the same way that
auxiliary views are created (see Chapter 11). Use the cutting plane line
to define the angle at which the view is to be taken and be sure to
include sectioning lines where material has been cut. Either complete
or partial auxiliary sectional views may be drawn. Figures 11-8 and
11-9 illustrate two auxiliary sectional views.

10-11 DIMENSIONING SECTIONAL
VIEWS

Sectional views are very helpful in presenting clear, well-defined
dimensions. In Chapter 6 we learned that it is considered poor practice
to dimension to hidden lines. Yet, there are many objects that contain
so many internal surfaces that it is impossible to dimension without
referring to hidden lines. By drawing sectional views, we open up to

Problems

215

Figure 10-20 An example of a dimensioned sectional view.

direct view the internal surfaces, thereby changing hidden lines to solid
lines which, in turn, give us solid, well-defined lines to dimension to.
Figure 10-20 illustrates how a sectional view may be dimensioned.
Note that the extension lines cross over the section lines. Also note the
small gap between the end of the extension line and the line that it is
defining on the object.

PROBLEMS

Assume that the following are sectional views of several different ob-
jects. Redraw the sectional views and add section lines. Each square on
the grid is 0.20 per side.

10-1

iSSi

216

10-2

Sectional Views

£hap. 10

Redraw the front view and replace the side view with a sectional view.
Each square on the grid is 0.20 per side.

10-3

.25DIA
TYP

.88 OIA

30'
2 PLACES

Problems

217

10-4

10-5

.63 R

1.00 R

too

75DJA

2.00

.50 [—

— H

/ | I— 1

r-t

---i

— ^ i i

aoo

30 v

218

10-6

Sectional Views

Chap. 10

.50DIA

.25 BOTH
SIDES

10-7

1,25 DIA

1.75 DIA

3.25

ALL FILLET AND ROUNDS = £R

Problems

219

10-8 Redraw the top view and replace the front view with a sectional
view.

75 DIA- 4 PLACES
1.63R

2.38R

.50 DIA

1.00DIA

2.00

L 1.00

10-9 Redraw the front and side views and add the appropriate sec-
tional views.

1.00

5,00

.38

.88

-< 2.00 **

"wf

1.50

1.00

,-i.

-* — 1.50-

-1C0--

-I

.33

5.00 -
REF

.38

1.50

n ■ i

/ — +_

h~h

.25— -J
— 4

38H-

HOLE

DIA

150

2 00

.08

1.00

1-00

.63

2 50

.50

3.63

213

.75

3.29

1.13

.75

3.00

.75

1.31

220

Sectional Views

Chap. 10

10-10 Redraw the following sectional view and add the appropriate
sectional views. Assume that all the pieces are round. Each square
on the grid is 0.20 per side.

Draw a front view and sectional view of the following. Each triangle on
the grid pattern is 0.20 per side.

10-11

T.88R

2.50DIA

1.25 DIA

1.00

Problems

221

10-12

10-13

2.00 Dl A

-2£z™^-

4.25

THE OBJECT IS
SYMMETRICAL

10-14

222

Sectional Views

Chap. 10

10-15 Draw a front and side view of the following object. Then draw
two sectional views, one as defined by cutting plane A and one
as defined by cutting plane B. Cutting plane A is located 1.25
from the left end of the object. Cutting plane B is located 1.00
from the right end.

1.00 R

END VIEW

AUXILIARY VIEWS

£^***r*^

i-—-..-. .^ :

■-.;<r^ •»»•*'

*^^^1

Figure 11-0 Photograph courtesy of TEREX Division, General
Motors Corp.

11-1 INTRODUCTION

Auxiliary views are any orthographic views other than the three
principal views. They are usually drawn to show the true shape of a sur-
face that otherwise would appear distorted in the normal front, top and
right side view format. For example, in Figure 11-1 neither the true
shape of surface 1-2-3-4 or the true shape of the V6 diameter hole is
shown in any of the given views. This means that even though three
views of the object are presented, from a visual standpoint, the drawing
is incomplete and therefore unsatisfactory.

Figure 11-2 shows the same object that was shown in Figure ll-l,
but this time using only two orthographic views: a front view and an
auxiliary view. The auxiliary view is an orthographic view taken per-
pendicular to surface 1-2-3-4. This two-view drawing is actually more
effective in its presentation of the object than is the three-view drawing.
Thanks to the auxiliary view, it defines the true shape of surface 1-2-
3-4 and the Vi" diameter hole as well as all other necessary information.
Deciding when and where to use auxiliary views depends on the
object being presented and on how its individual surfaces are positioned.
Always use auxiliary views to add clarity to your drawings and thereby
to make the technical information you are presenting easier to under-
stand.

Figure 11-1 Three views of an inclined surface.

224

Sec. 1 1 -2

Reference Line Method

225

Figure 11-2 A front view and an auxiliary view of the object
presented in Figure 11-1.

11-2 REFERENCE LINE METHOD

Two methods may be used to create auxiliary views: the reference
line method, explained in this section, and the projection theory method,
explained in the next section. Figure 11-3 is a sample problem in which
you are given two views and are asked to create an auxiliary view that
clearly presents surface 1-2-3-4-5. Figure 11-4 is the solution and was
derived by using the reference line method as follows:

GIVEN: Front and side views.

PROBLEM: Draw an auxiliary view using the reference line meth-
od.

GIVEN: Front and side views.

PROBLEM: Draw an auxiliary view using the projection theory

method.

9,10

9,4
72 S3

5,10

Figure 11-3

226

Auxiliary Views

Chap. 11

SOLUTION: Using the reference line method:

1. Draw a vertical line between the front and right side views and
draw a line parallel to surface 1-2-3-4-5-6. Define the vertical
line as reference line 1. Define the line parallel to surface 1-2-
3_4-5 a s reference line 2.

Reference
Line 2

1 6

Reference Line 1

Figure 11 -4(a)

2. Label points 1, 2, 3, 4, 5, 6, and any other points you feel
you'll need in both the front and right side views.

3. Project all points in the front view into the auxiliary views by
drawing very light lines perpendicular to reference line 2 from
the front view points into the area where the auxiliary view will
be.

Se*. 11-2

Reference Line Method

227

4. Using either dividers or a compass, transfer the points from the
right side view to the auxiliary view by transferring the. per-
pendicular distance from reference line 1 to the point, to refer-
ence line 2 along the appropriate point projection line created
in step 3. This is possible because the distance between refer-
ence line 1 and the right side view and the points is the same as
the distance between reference line 2 and the auxiliary view.
Label all points in the auxiliary view.

5. Lightly draw in the auxiliary view by lightly connecting the
appropriate points. Check your work.

6. Erase all excess lines, point labels, and smudges and draw in all
lines to their final configuration and color.

9,10

5,10

Figure 11 -4(d)

228

Auxiliary Views

Chap. 1 1

Note that surfaces 4-5-9-10 and 2-3-8-7 are distorted in the
auxiliary view.

Figures 11-5 and 11-6 are further examples of auxiliary views
drawn by using the reference line method.

Figure 11-5 An auxiliary view created using
the reference line method.

Figure 11-6 An auxiliary view created
using the reference line method.

11-3 PROJECTION THEORY METHOD

The projection theory presented in Chapter 4 may also be applied
to auxiliary views. The problem of Figure 11-3 is again presented, but
this time it is solved by using the projection theory method. The solu-
tion is illustrated in Figure 11-7 and was derived by using the following
procedure:

SOLUTION: Using the projection method:

1. Draw a vertical line between the front and right side views and
draw a line parallel to surface 1-2-3-4-5-6. Draw the lines so
that they intersect. Label the intersection point 0. Through
point draw two more lines: one perpendicular to the vertical
line (therefore a horizontal line) and one perpendicular to the
line drawn parallel to surface 1-2-3-4-5-6.

Line Parallel

to Surface 1-2-3-4-5-6

Line

Point

Vertical Line

Figure ll-7(a)

Project the points labeled in the side view into the area where
the auxiliary view will be by first drawing vertical projection
lines from the points to the horizontal line drawn in step 1.
Then, using a compass set on point 0, draw projection arcs
which will continue the vertical projection lines from the
horizontal line to the line perpendicular to the line parallel to
surface 1-2-3-4-5-6. Continue the projection lines parallel
to surface 1-2-3-4-5-6 as shown.

4
3

Figure 11 -7(b)

229

230

Auxiliary Views

Chap. 11

3. Project the points from the front view by drawing lines per-
pendicular to the line drawn parallel to surface 1-2-3-4-5-6.
Label the intersections of these projection lines with the ones
drawn in step 2 with the appropriate numbers.

Figure ll-7(c)

4. Erase all excess lines, point labels, and smudges and draw in all
lines to their final configuration and color.

5.10

Figure 11 -7(d)

Sdc. 1 1-5

Partial Auxiliary Views

231

Note that the solution derived by the projection theory method is
exactly the same as the solution derived by the reference line method.
Either method will generate an accurate answer and the choice of which
method to use depends on the preference of the individual draftsman.

11-4 AUXILIARY SECTIONAL VIEWS

Auxiliary sectional views are a combination of an auxiliary view and
sectional view. They are orthographic views taken through an object at an
angle defined by a cutting plane line. They adhere to the same rules and
format given for sectional views in Chapter 10, and they are drawn for
the same reasons: to expose surfaces that are hidden from direct view in
the regular front, top, and right side views.

Figure 11-8 is an example of a drawing that contains an auxiliary
sectional view. Figure 11-9 is an example of a drawing that contains a
partial auxiliary sectional view. Either the reference line or projection
line method may be used to create auxiliary sectional views.

SECTION A-A

Figure 11-8 An auxiliary sectional view.

Figure 11-9 A partial auxiliary sectional view.

11-5 PARTIAL AUXILIARY VIEWS

Auxiliary views are helpful in clarifying drawings, but their use
does have drawbacks. For example, surface 1-4-6-5 which appeared
true size in the top view of Figure 11-1 appears distorted in the auxiliary
view in Figure 11-3. The same is true of surface 2-7-8-3. By trying to
create a view that will clarify one surface, we have distorted two other
views. To eliminate distortion in the principal views, we have created
auxiliary views which in turn have created other distortions.

The solution is to use partial auxiliary views. Figure 11-10 shows
the same object that was shown in Figures 11-1 and 11-2 and was
drawn using a front view and a partial auxiliary view. As the name

232

Auxiliary Views

Chap. 11

Not included

Figure 11-10 Front and partial auxiliary views of an object.

implies, a partial auxiliary view is only part of a complete auxiliary
view. Partial auxiliary views enable you to limit your auxiliary view to
one specific surface or part of a surface, thereby eliminating the need
to draw surfaces that have become distorted in the auxiliary views.
If only one complete surface is shown in the partial auxiliary view,
as is the case in Figure 11-10, break lines need not be shown. If how-
ever, part of a surface or more, than one surface is to be drawn, break
lines are shown.

11-6 SECONDARY AUXILIARY VIEWS

It is sometimes necessary to draw an auxiliary view of an auxiliary
view. This occurs when the first auxiliary view does not completely
define or does not clearly present the surface being studied. For example,
Figure 11-11 shows a front, top, right side, and auxiliary view of an
object that contains an oblique surface (surface 1-2-3). Despite the
great number of views taken of the object, none of the given views
shows the true shape of surface 1-2-3. To present a true shape of sur-
face 1-2-3, we must use a secondary auxiliary view.

The true shape of surface 1-2-3 will only be shown in an ortho-
graphic view taken at exactly 90° to the surface. To help you visualize
this concept, think of an airplane in flight. If the airplane is flying
directly away from you, parallel to your line of sight (0°), it will give
little or no indication of its true speed. It will simply seem to slowly
disappear. If, however, the airplane is flying directly across your line of
vision (90°), it will give a correct indication of its true speed. Similarly,
only when a line or a plane is directly across your line of vision (an
orthographic view taken at exactly 90° to your line of vision) can you
see its true shape.

Figure 11-11 What is the true shape of surface 1-2-3? None of
these views define it.

But how can we be assured that our secondary auxiliary view is
taken at 90° to the surface? If we want our secondary view to be 90°
to a surface, the first auxiliary view must be taken 0° to the surface
because each auxiliary view will be 90° to the previous one.

To draw an auxiliary view that is at 0° to the surface (an end
view of the surface), we must identify a true length line on the sur-
face. A true length line is the only line on the surface whose angle
relative to the principal plane lines we know exactly. Because we know
the exact angle of a true length line relative to the principal plane lines,
we know the angle at which to draw an auxiliary view which will be an
end view of the line and therefore an end view of the surface in which
the line is located.

A true length line is found by the following axiom:

An orthographic view of a line shows the true length
(TL) of that line if one of the other orthographic views
of that line is parallel to one of the principal plane lines. Axiom 1 1 -1

Figure 11-12 illustrates this axiom. Note that so long as one of the
given orthographic views is parallel to one of the principal plane lines,
the other view of the line is a true length. If none of the views of the
line is parallel to either principal plane line, then none of the given
views is a true length. Also note that because one of the lines in a sur-
face is true length, it does not mean that all the other lines in the
surface are true length.

In the example of Figure 11-11, line 1-2 is true length in the top
view, line 1-3 is true length in the front view, and line 2-3 is true length
in the right side view. We could use any one of these lines to generate
an auxiliary view that is 0° to the surface 1-2-3. Line 1-2 was used for
this example.

233

<> 'i

»&■■<!

i 3

4-^

234

Sec. 1 1 -6

Secondary Auxiliary Views

235

Figure 11-13 is the solution to the problem presented in Figure
11-11 and was derived by using the following procedure:

SOLUTION:

1. Identify in one of the given views a true length line. In this
example line 1-2 meets the criterion set by axiom 11-1.

Figure 11-13(»)

2. Extend line 1-2 and draw lines parallel to the extension of line
1-2 throughout the other known points on the surface.

Figure 11 -13(b)

236

Auxiliary Views

Chap. 11

Draw in the principal plane line between the two given views
and label it reference line 1. Also draw a line somewhere along
the extension lines drawn in step 2. The line must be perpen-
dicular to those lines. Label it reference line 2.

Reference Line 2

: : ^ — Reference Line 1

Figure 11-1 3(c)

4. Measure the distance from reference line 1 to point 1 in the
view that contains line 1-2 parallel to the principal plane line.
Transfer this distance to reference line 2 as shown. Make sure
that you transfer the distance to the line that was originally
extended through point 1. Do the same with all other points
in the surface. Measure the distance from the point to reference
line 1, and then transfer this distance to reference line 2 as
shown.

Figure 11 -13(d)

Sec. 11-6

Secondary Auxiliary Views

237

5. Using appropriate point numbers, label the first auxiliary view
you have now generated.

End view of
Plane 1-2-3

Figure 11-1 3(e)

6. Draw lines perpendicular to the auxiliary view through all
points on the surface as shown. Draw a line parallel to the end
view of the surface and label it reference line 3 .

Reference Line 3

Figure 11 -13(f)

238

Auxiliary Views

Chap. 1 1

7. Measure the distance from reference line 2 to point 1 in the
view in which line 1-2 appeared true length. Transfer this
distance to reference line 3 as shown. Do the same with all
other points in the surface.

8. Label the secondary auxiliary view of the surface with the
appropriate point numbers and darken in all lines to the final
color and configuration. Leave on all construction lines unless
you are specifically told to erase them. This will make it easier
for someone to check or follow your work.

True Shape of
Plane 1-2-3

Figure 11-1 3(g)

Figure 11-14 is the solution to the problem stated in Figure 11-11,
except that in Figure 11-14 line 2-3 was used to generate the first
auxiliary view. The problem was solved by using the procedure out-
lined for Figure 11-13. Note that the true shape of surface 1-2-3 is
exactly the same as that generated in Figure 11-13. Study and carefully
verify how each point was transferred from reference line to reference
line.

Sometimes none of the given lines that define a surface is of true
length. This does not mean that a secondary auxiliary view of the sur-
face cannot be created. It simply means that we have to create a true
length line from the given information and then proceed as before. For
example, the surface 1-2-3 pictured in Figure 11-15 contains no true
length lines and yet the problem asks us to find the true shape of that
surface which we know can only be accomplished through a secondary
auxiliary view.

Sec. 1 1 -6

Secondary Auxiliary Views

239

Figure 11-14 The true shape of plane 1-2-3 found by using the
true length view of line 2-3.

GIVEN: Front and top views.

PROBLEM: Draw the true shape of plane 1-2-3.

NO True Length Lines

Figure 11-15

To create a true length line in surface 1-2-3, first draw a line in
one of the views that is parallel to one of the principal plane lines. Then
project this line into the other view of the surface. In this example the
new line was labeled 1-x where point x lays along the known line 2-3.
To project point x from the top view into the front view, draw a line
parallel to the line drawn between the two known point 1 's and perpen-
dicular to the principal plane line from point x in the top view to a

240

Auxiliary Views

Chap. 11

point of intersection with line 2-3 in the front view. The solution to
the problem is completed as previously outlined based on the true
length line Q-x. Figure 11-16 is the solution to the problem stated in
Figure 11-15.

SOLUTION:

Figure 11 -16(a)

Figure 11 -16(b)

Figure ll-16(c)

True Shape

Figure 11 -16(d)

Problems

241

PROBLEMS

Redraw the following objects and add the appropriate auxiliary views:
11-1

'II

" x ^— jiaiuL_

v.zl/- - -----r

-- — -■-{-

i_ «_™ — i ■■■

... .. M ....

"^s /

^t v iT

. *S£ —- <rfi°

/ / N

V j ^ % J

|T i t t -L

' / V

t .A-2 £ [j

__ i__j__i --- J

t 1

11-2

HEXAGON
1.75 ACROSS FLATS

50X.50 SQUARE HOLE
Perpendicular to
inclined surface

11-3

| | j | fl^C|r^|A|-|SjffLjA|C|E|S| | |_| | | | | | | | | | | [ _

3 *."~ w "*"

P v* 1

P L

V N

"' ^r j l

S \

.„. z~.~^y:z.. ____j^ j.l-..- i:

242

11-4

Auxiliary Vitws

Chap. 11

1.25

11-5

11-6

2.00

[« 2.00 -

1.38-*
-.89

45
* 2.00 »-

-.50

11-7

s s

11-8

2 LARGE HOLES-.75DIA
1 SMALL HOLE -.50 Dl A

1.94

.75

11-9

11-10

45'

1,75
.25-

ze:

3fr

I — «*

138

^-.88

•

11-11

.38 Dl A -12 PLACES

2,00

1.06

244

Auxiliary Views

Chap. 11

Using a secondary auxiliary view, derive the true shape of the following
planes. Each square of the grid is 0.20 per side.

11-12

C ■ **■ *

\ ^^"^ 1 ill—

J ^^fc #1

*~ \i ***■* *

\ rf** J

*s 1- *^

.j 4

i« -

3-S**

t- -*, -r~ -

-i - ^*^1

/ m ^m ' ^ \&1WL

^t* - ** ~^L

— — £-»■=

11-13

._!.

Ikf'

L_ ' 4 ^"^'-~

..s„

*■ h » I

r 3

r "7

-""""■"^-O

JP'*'

, . £«tf±

Draw sufficient views to completely define the following objects. In
each case, include a secondary auxiliary view of the oblique surface.

11-14

Problems

245

11-16

.25 0! A

19 OIA

FASTENERS

Figure 12-0 Photograph of an Allison 501-M62B turboshaft
engine courtesy of Detroit Diesel Allison Division of General
Motors Corp.

12-1 INTRODUCTION

There are two basic fasteners: mechanical and nonmechanical. Me-
chanical fasteners include bolts, rivets, and screws and, from a design
standpoint, they are usually stronger, easier to work with, and more
easily replaced than nonmechanical fasteners. Nonmechanical fasteners
include glues, epoxies, tapes, and so on, and they are usually less expen-
sive, lighter, and require less installed space than do mechanical fasteners.

This chapter deals exclusively with mechanical fasteners. Non-
mechanical fasteners are not drawn, but they are noted on a drawing
as shown in Figure 12-1. Mechanical fasteners, however, have specific
representations that must be clearly and accurately drawn.

EPOXY PER
SPEC NO. 56A

Figure 12-1 A call out for a nonmechanical fastener.

12-2 THREAD TERMINOLOGY

Figure 12-2 illustrates some of the basic terms used to describe a
thread. These terms are common to all kinds of threads and will be
referred to throughout the chapter.

Pitch, P

Major Diameter, D

1 — Minor Diameter

Figure 12-2 Some basic terms used to describe a thread.

247

248

Fasteners

Chap. 12

The pitch of a thread is equal to 1 over the number of threads per

inch.

P -

Number of threads per inch

(12-1)

A thread made with 20 threads per inch, for example, has a pitch of
0.05".

P - - - 0.05

A thread with eight threads per inch has a pitch of 0.125'

P = -=- = 0.125

1 2-3 THREAD NOTATIONS

-i--2pUNF-2

\ V-ciasa of nt

\ ^Thread Category
Threads per l«ch

Major Diameter

Figure 12-3 The definition of a thread
notation.

Figure 12-3 shows a typical thread notation and a definition of
each term The terms major diameter and threads per inch (pitch) have
already been explained in Section 12-2 and Figure 12-2. The terms
thread category and class of fit require further explanation.

Threads are generally manufactured to either National Coarse or
National Fine standards, although there are several other categories of
thread standards (Unified Extra Fine, for example). These standards are
internationally agreed upon manufacturing specifications that result in
products of uniform quality and interchangeability. From a drawing
standpoint, there is no difference between any of the standards, for
they all use the same representations.

Class of fit refers to the way in which two threads match each
other. There are four categories: classes 1, 2, 3, and 4. The higher the
number, the better quality the match-up. Class 1 is a very sloppy fit;
class 2 is the most commonly manufactured fit and is generally ac-
ceptable in most design situations; classes 3 and 4 are rarely specified
because they are very exact and very expensive.

12-4 THREAD REPRESENTATION

There are three ways to represent threads on a drawing: detailed,
schematic, and simplified. From a drawing standpoint, each representa-
tion has advantages and disadvantages. The detailed representation is
very easy for the reader to understand, but it is very time-consuming
to draw. The simplified representation is very easy to draw, but to the
uneducated reader, it is very confusing. The schematic representation
is a compromise-fairly easy to draw and fairly easy to read, but it is
still inexact and time-consuming. The representation chosen will de-
pend on the specific shop or drafting requirements applicable.

Sec. 12-4 Thread Representation 249

Simplified Representation (Figure 12-4):

(a) Define the major diameter, thread length, and shaft length
of the desired thread.

Shaft Length

-Thread Length

-Major Diameter, I

Figure 12-4(a) Simplified thread representation.

(b) Draw a 45°-chamfer 1/16 or 1/8 long on the end of the
threaded portion of the shaft. The choice of 1/16 or 1/8
depends on which looks better.

i-i

Figure 12 -4(b)

-^OT

16 U 'T

Figure 12-4(c)

(d) Darken in the visible lines and add the appropriate thread
call out.

Y"16UNC-2A

Figure 12-4(d)

250

Fasteners

Chap. 12

Schematic Representation (Figure 12-5):

(a) Define the major diameter, thread length, and shaft length of
the desired thread.

Shaft Length

Thread Length

1 — Major Diameter, D
Figure 12-5(a) Schematic thread representation.

: : ■

(b) Draw parallel lines as shown. Draw these lines extremely
lightly because they will be erased later. The choice of 1/16
or 1/8 depends on which looks better.

1 rt r 1

i6 or T

Figure 12-5(b)

(c) Draw lines perpendicular to the lines drawn in step (b) as
shown. If 1/16 was used in step (b), space them 1/16 apart. If
1/8 was used in step (b), space them 1/8 apart.

"1M

1S°'T

Figure 12-5(c)

(d) Draw 45°-chamfers at the threaded end of the shaft as shown.
Draw lines parallel to and halfway between the lines drawn
in step (c). Start and end these lines as they intersect the lines
drawn in step (b).

Figure 12 -5(d)

Sec. 124

Thread Representation

251

(e) Darken the lines created in step 4 and all visible lines as
shown. Add the appropriate thread call out.

^--16UNC~2A

Figure 12-5(e)

If desired, the spacing of the lines drawn in step (c) may be made
exactly equal to the thread pitch.

Detailed Representation (Figure 12-6):

(a) Define the major diameter, thread length, and shaft length of
the desired thread.

Shaft Length

-Thread Length

—Major Diameter, D
Figure 12-6(a) Detailed thread representation.

(b) Along the top edge of the shaft mark off as many distances
P as will fit within the desired thread length. Mark off a
distance of x hP along the bottom edge.
Note: This is a right-hand thread. When the designated thread
is a left-hand thread, the P distances would be marked off
along the lower edge and the x hP distance along the top edge.

Figure 12-6(b)

252

Fasteners

Chap. 12

(c) Connect the first P distance with the l AP distance. Then draw
lines, parallel to this line, through each of the P distances as
shown.

Figure 12-6(c)

(d) Draw short 60° -lines as shown.

■No line
Figure 12-6(d)

(e) Draw short 60° -lines so that they intersect the lines drawn in
step (d) as shown.

Figure 12 -6(e)

(f) Connect the intersections of the 60°-lines as shown. These
lines are not parallel to the lines drawn in step (c).

Figure 12-6(f)

(g) Darken the lines as shown and add the appropriate thread call
out.

1- 16UNC-2A

Figure 12-6(g)

Sec. 1 2-5 Threads in a Sectional View

12-5 THREADS IN A SECTIONAL VIEW

253

Figure 12-7 shows the three different thread representations as
they appear in a sectional view. Note that the simplified representation
includes hidden lines. Hidden lines are drawn in sectional views when a
simplified representation is used and in all end views of threaded holes
regardless of the representation.

fc^^j

Figure 12-7(a) Simplified representation.

Figure 12-7(b) Schematic representation.

Figure 12-7(c) Detailed representation.

254

Fasteners

Chap. 12

12-6 THREADS

There are several different kinds of threads: square, acme, knuckles,
sharp V, and others. Figure 12-8 shows profiles of these threads.

A double thread has two threads cut on the same shaft. When it is
rotated, it advances or recedes twice as fast as a single thread (one
revolution of a double thread will transverse twice the distance traveled
by one revolution of a single thread). Double threads may be cut in any
thread-square, UNC, UNF, and so on. Figure 12-9 includes a double
thread drawn by using simplified representation. Note how the thread
note is written and that the picture portion of the drawing is the same
as for single threads.

SQUARE

ACME

KNUCLE

SHARP V

Figure 12-8 Various thread profiles.

-^-12 UNC-2A, DOUBLE
x 2.00 LONG

Figure 12-9 A double thread call out and simplified representa-
tion.

Most threads are right-hand threads-that is, they advance when
they are turned clockwise. There are also left-hand threads. The oxygen
lines in most hospitals are made with left-hand threads as a safety pre-
caution to prevent an accidental mix-up with other gas lines. The
schematic and detailed representations are drawn the same for left- or
right-hand threads. Only the notation is amended to include an "LH

Sec. 12-8

Threaded Holes

255

for left-hand threads. It is assumed that a thread is a right-hand thread
if LH does not appear. Figure 12-10 illustrates a call out note for a
left-hand thread.

f -18UNF

2A-L.H.X.75 LONG

Figure 12-10 A left hand thread call out and schematic repre-
sentation.

The detailed representation of a left-hand thread is different from
the detailed representation of a right-hand thread. To draw a left-hand
thread, use the same procedure but change the initial P/2 offset shown
in step 2 of Figure 12-6 from the top edge to the bottom edge of the
thread.

12-7 TYPES OF BOLTS AND SCREWS

Figure 12-11 illustrates several of the many different mechanical
fasteners that are commercially available. The exact size and shape spec-
ifications are available from the manufacturers.

^=U=p,

Figure 12-11 Different types of mechanical fasteners, (a) Flat-
head, (b) Fillester Head, (c) Round Head, (d) Oval Head.

12-8 THREADED HOLES

When you draw a threaded hole representation, it is important to
know how such a hole is created. First, a hole, called a pilot hole, is
drilled. This hole is then tapped (threads are cut into the surface of the
pilot hole). Holes are not usually tapped all the way to the bottom of
the pilot hole because this would cause severe damage to the tapping

Pilot hold depth
Thread dapth

Oft

Figure 12-12 A tapped hole.

bit (although special tapping bits are available that will tap to the bot-
tom of a pilot hole).

When you draw a threaded hole, always show the untapped por-
tion of the pilot hole as illustrated in Figure 12-12, The pilot hole
usually extends the equivalent of two thread lengths beyond the tapped
portion of the hole. For example, if we wish to draw a threaded hole in
which the thread depth is to be 3 and the thread type is to be 1-8UNC-2,
we would first calculate the depth of one thread by using Equation
(12-1):

P =

Number of threads per inch

1_
" 8

P = 0.125

2P = 0.250

See Figure 12-13 for an example of this.

We would then calculate the depth of the pilot hole by adding the

total length of the thread to the equivalent of two thread lengths.

total thread length + 2P = pilot drill depth

(12-Z)
3.000 + 0.250 = pilot drill depth

1.00

3.25

3,00

-4J

-J

Figure 12-13 An orthographic view, a
sectional view using the simplified repre-
sentation, and a sectional view using the
schematic representation of a 1-8UNC-2
X 3 thread.

256

Sec. 1 2-8

Threaded Holes

257

If we wished to draw a threaded hole with a 3/8-16UNC-2 thread
cut to a depth of 1.38, the calculations would be as follows:

From Equation (12-1)

P =

1
16

P=0.06

2P = 0.12

From Equation (12-2)

1.38 + .12 = pilot drill depth

1.50 = pilot drill depth

Figure 12-14 illustrates a threaded hole with a screw assembled
into it. Note how the bottom of the screw is distinguished from the
threads by the 45°-chamfers and also note that the threads extend be-
yond the bottom of the screw. Threads usually extend at least two
thread lengths beyond the bottom of a screw to prevent the screw from
bottoming and jamming in the hole.

Bottom edge of screw

Figure 12-14 A threaded hole with a screw assembled into it.
(a) orthographic view, (b) simplified representation, (c) schematic
representation.

To draw a threaded hole with a fastener assembled in it, calculate
the thread depth from Equation (12-3) and the pilot hole depth from
Equation 12-2.

threaded hole depth = fastener depth + 2P

(12-3)

25S

Fasteners

Chap. 12

Length

H»

For example, to draw a threaded hole for a 3 / 4 -10UNC-l X 2.50 ma-
chine screw, first calculate the threaded length by using Equation (12-1).

P = 0.10

2P = 0.20

Calculate the threaded hole depth'by using Equation (12-3).

threaded hole depth = 2.50 + 0.20 = 2.70

Finally, calculate the pilot hole depth by using Equation (12-2).

pilot hole depth = 2.70 + 0.20 = 2.90

A table of pilot hole diameters for various thread diameters is in-
cluded in the Appendix.

12-9 DRAWING BOLT AND
SCREW HEADS

Figure 12-15 illustrates how to draw a hex head bolt. The proce-
dure used is as follows :

& 4> & 4> fk

&-, III

Figure 12-15 How to draw a hex head bolt.

(a) Define the diameter and length of the bolt.

(b) Draw a circle of IV2D diameter as shown. Draw a line parallel
to the top of the bolt shank as a distance 2/3D as shown.
Note: The term 1V6D means one and one half times the di-
ameter. Similarly, the 2/3D. If, for example, the diameter of
the bolt were l A, 1V£D would equal

,l n 3 A\ 3

Sec. 12-9

Drawing Bolt and Screw Heads

2S9

2/3D would equal

(f)

(g)

3 3 \2/

Circumscribe a hexagon around the IVfcD circle.
Project the hexagon's comers as shown.
Draw a line 60° to the horizontal through the intersection of
the outside corner projection line and 2/3D line created in
step (b) such that it crosses the center line of the bolt. Do the
same for the other corner intersection. Label the intersection
of the two 60°-lines point 1.

Draw a 60°-line through each of the intersections of the in-
side projection lines and the 2/3D line created in step (b).
Label the intersections of these 60° -lines with those created
in step (e) points 2.

Using point 1 and both points 2 as compass points, draw arcs
as shown. Darken in the appropriate lines and add the desired
thread notation.

Figure 12-16 illustrates how to draw a square head bolt. The pro-
cedure used is as follows :

Length

«*■

**1

£*%

to. c. d.

Figure 12-16 How to draw a square head bolt.

(a)
(b)

(f)

Define the diameter and length of the bolt.

Draw a circle of IV2D diameter as shown. Draw a line parallel

to the top of the bolt shank at a distance 2/3D as shown.

Circumscribe a square around the IV2D circle.

Project the square's corners as shown.

Draw 60°-lines through the intersection of the projection

lines drawn in step (d) with the 2/3D line drawn in step (b).

Label the two intersections of the 60° -lines points 1.

Using the points 1 as compass centers, draw in the arcs as

shown. Darken in the appropriate lines and add the desired

thread notation.

26Q

Fasteners

Chap. 12

a. b.

Figure 12-17 How to draw hex and square nuts.

Nuts are drawn by using the same procedures as for bolt heads ex-
cept that they are 7/8D high instead of 2/3D high. Figure 12-17 il-
lustrates a hex and square nut.

12-10 RIVETS

Rivets are metal fasteners that are commonly used to hold sheet
metal parts together. Although they are inexpensive and light weight,
they are not as strong as screws or bolts. Rivets are not reusable and
once they are placed in an assembly, they can only be removed by

drilling.

Figure 12-18 illustrates two of the many representations used to
call out rivets on a drawing. The detailed representation in the top view
consists of circles with diameters equal to the diameter of the rivet's
head. The side view is as shown. In the top view the schematic represen-
tation consists of short, perpendicularly crossed lines that locate the
center of the rivet. The side view looks like a center line of a hole,
except that it always ends with a short line.

Detailed

Schematic

ran

Figure 12-18 Rivet representations.

Sec. 12-11

Welds

261

The meaning of the call outs for schematic representations is
illustrated in Figure 12-19. The actual identification letter designa-
tions (BJ, CX, HY, and so on) vary from company to company, al-
though most aircraft companies use the National Aircraft Standards
(NAS).

*«

A«*

BJ 4

Figure 12-19 The meaning of schematic representation rivet
callouts.

A long row of rivets, provided that the rivets are all exactly the
same kind, may be called out by calling out only the first and last rivet
in the row. Figure 12-20 illustrates this kind of rivet call out.

Figure 12-20 How to call out rows of rivets.

12-11 WELDS

Welds are usually called out on a drawing by notes such as shown
in Figure 12-21. There are many different welds. Interested students
are referred to the American Welding Society, 2501 N.W. 7th St., Miami,
Florida 33125.

*°

'«

°r

"•/»

1—,

■ SPOT WELD

Figure 12-21 Weld call outs per standards set by the American
Welding Society.

PROBLEMS

Redraw the following and add the appropriate fasteners. Use the
representation specified by your instructor. Each square on the grid
pattern is 0.20 per side.
12-1

262

Problems

263

12-2

-|-16UNC-2Axll-HEX HEAD BOLTS

Thread is ~ long

12-3

■

r t j r

JfcJ JL

^.f — ^^^BlB2-LtL:^p

^ 7 I1ECJD3JI

^ f

**"

-J'**

I3EHZ" > s dC u

aCifia — U .

12-4

1 : T1 1

i - s;:ai«£.'2^S.3- IJ\1 HEjiiL-iJL'JJtftl I

1 V-^' °

t "V "' "'

v J „

__3 ,

- ■ 1 _L

264

Fasteners

Chap. 12

12-5 Redraw the following sectional view and add the following
fasteners:

(a) 5/16-18UNC-2A X 1.25 hex head bolt

(b) 7/16-14UNC-2A X 1.38 square head bolt

(d) 9/16-18UNF-3A X 1.00 square head bolt

12-6 The shop complains that the following fastener call outs are in-
correct because the heads interfere, that is, bump into one another.
Prepare a layout to verify if this is true. If it is true, how would
you alleviate the interference?

^-14 UNC-2AX1-1- HEX HEAD

^-14UNC-2Axl-£-

FILLISTER
HEAD

Problems

265

12-7 Redraw the following figure and add the appropriate rivet call
outs. Make the end rivets of each row (first and last rivet) BJ6s
and all other rivets BJ4s.

32*4 * 4

AL ANGLE

16GAGE AL
(.06 THK)

METRICS

Figure 13-0 Photograph courtesy of Volkswagen werk, Wolfsburg,
Germany

13-1 INTRODUCTION

Many large corporations, both in the United States and in other
countries, are multinational corporations. They operate plants, buy
goods, and sell products in many countries. Olivetti-Underwood, for
example, is an Italian company headquartered in Ivrea, Italy, but it owns
and operates manufacturing plants in Spain, the United Kingdom, the
United States, Argentina, Brazil, Colombia, and Mexico, and it sells
its products worldwide.

Because so many companies operate internationally, engineers
and draftsmen must be prepared to exchange technical information
internationally. This may be difficult, not only because of the language
differences, but also because of the different systems used to measure
and present technical information. In the United States we use the
English system of measuring (feet and inches) and third angle projec-
tions for presenting orthographic views. Most other countries use
the metric system of measuring (meters and millimeters) and first
angle projections for presenting orthographic views.

Because the metric system is easier to use than the English system,
all major nonmetric countries have started to change their engineering
measuring systems to the metric system, but the change has not yet
been completed. In the United States the change has been slow,
primarily because of the enormous costs involved in replacing existing
nonmetric tools and machinery. Until the metric system becomes
universal, it is important that draftsmen know how to work comfortably
in both systems. This chapter will explain the metric system and first
angle projection and then it will compare them with the English system
and third angle projection.

13-2 THE METRIC SYSTEM

In the metric system measurements of length are based on a fixed
unit of distance called a meter. A meter is slightly longer than a yard.
A meter is divided into smaller units called centimeters and millimeters.
There are 100 centimeters or 1000 millimeters to a meter. Most me-
chanical measurements in the metric system are made by using milli-
meters just as most mechanical measurements in the English system are
made by using inches.

The symbol for a millimeter is mm (5 mm, 26 mm, and so on).
Figure 13-1 shows a millimeter scale along with a few sample measure-
ments.

To convert a given millimeter value to meters, divide the given
value by 1000, which is the same as shifting the decimal point three

267

268

Metrics

Chap. 13

1 234

6789

TITT

1
(10)

Figure 13-1 A millimeter scale with some sample measurements.

places to the left. For example,

423 mm = how many meters?
423

1000

■ .423 m

To convert a given meter value to millimeters, multiply the given
value by 1000, which is the same as shifting the decimal point three
places to the right. For example,

5.1 m = how many millimeters?

(5.1)(1000) = 5100 mm

All intermetric distance conversions are accomplished in a similar
manner. Remember that there are 10 millimeters to 1 centimeter, 100
centimeters to 1 meter, and 1000 millimeters to 1 meter.

13-3 CONVERSION BETWEEN
MEASURING SYSTEMS

To convert millimeters to inches or inches to millimeters, use the
following equality:

25.4 mm - 1 inch

If you are given a value in millimeters and wish to convert it to an inch
value, divide the millimeter value by 25.4. For example,

354 mm = how many inches?

354

25.4

= 13.94 inches

* * *

Sec. 13-4 Conversion Tables 269

10 mm = how many inches?
10

25.4

= 0.394 inch

If you are given a value in inches and wish to convert it to a millimeter
value, multiply the inch value by 25.4. For example,

3.20 inches = how many millimeters?

(3.20)(25.4) = 81.28 mm

* * *

0.68 inch = how many millimeters?
(0.68)(25.4) = 17.27 mm

If you are given a fractional inch value and wish to change it to a milli-
meter value, you must first change the fractional value to its decimal
equivalent in inches and then multiply the decimal value by 25.4. For
example,

7
6— inches = how many millimeters?
8

7
6— inches = 6.88 inches

(6.88)(25.4) = 174,75 mm

* * *

— inch = how many millimeters?
16

— — inch = . 56 inches
16

(.56)(25.4) = 14.22 mm

13-4 CONVERSION TABLES

This section contains two conversion tables: one for converting
inches to millimeters (Table 13-1), and one for converting millimeters
to inches (Table 13-2). Conversion tables enable you to convert given
values directly without having to go through extensive calculations. The
tables, however, are limited and any values not included in them must
be converted mathematically.

To use the inches to millimeters table, break the given value into
its whole number, tenths, hundredths, and thousandths values and

Whole Numbers

Ten

ths

Hundreds

Thousands

25.4

2.54

.01

.254

.001

.02 54

50.8

5.08

.02

.508

.002

.0508

(0.<£.

7.62

.03

.762

.003

.0762

101.6

.**

10.16

.04

1.016

.004

,1016

127.0

12.70

.05

1.270

.005

.12 70

152.4

15.24

.06

1.524

.006

.1524

177.8

17.78

.07

t.7?8

.007

.1778

203.2

20.32

.08

2.032

.008

.ZU32

228.6

22.86

.09

2.2 86

.009

.2286

254.0

1.0

25.40

.10

2.540

.010

.2 540

"fl

279.4

304.8

330.2

355.6

381.0

406.4

431.8

457.2

482.6

508.0

533.4

558.8

584.2

o09,6

Table 13-1 Inches to millimeters.

.039

1.024

2.008

2.992

079

1.063

2.047

3.032

.118

1.102

2j087

3.071

.158

1.141

2.1 26

3.110

.197

1.181

2,165

3.150

.236

1.221

2.205

3.189

.276

1.260

2.244

3,228

.315

1.300

2-284

3.268

.354

1.339

2.323

3.307

.394

1.378

2.362

3.347

.433

1.417

2.402

3.386

.472

1.457

2.441

3.425

.512

1.496

2.480

3.464

.551

1.535

2.520

3.504

.591

1.575

2.559

3.543

.630

1.614

2.598

3.583

.669

1.653

2,638

3.622

709

1.693

2,677

3.661

,748

1.732

2.717

3.701

.787

1.772

2.756

3.740

.827

1.811

2.795

3.780

.866

1.850

2.835

3.818

.906

1.890

2.874

3.858

.945

1.929

2.913

3.898

.984

1.969

2.953

100

3.937

100

3.937

600

23.622

200

7.874

700

27.559

300

11.811

800

31.496

400

15.748

900

35.433

500

19.685

1000

39.370

Table 13-2 Millimeters to inches,

270

Sec. 13-4

Conversion Tables

271

convert each separately. Then add the individual values together to
form a final equivalence value. For example,

Given 3.472 inches

How many millimeters is this equal to?

Whole number value 3.000 = 76.2000

Tenths value 0.400 = 10.1600

Hundredths value 0.070 = 1.7780

Thousandths value 0.002 = 0.0508

88.1888

Values
from
Table 13-1

Therefore^

3.472 inches = 88.1888 mm, or approximately 88 mm

Table 13-1 is only good for decimal values. Fractional values
must be converted to decimal equivalents before they may be con-
verted into millimeters. For example,

Given — inch
8

How many millimeters is this equal to?

— inch = 0.375

Whole number value 0.000

Tenths value 0.300

Hundredths value 0.070

Thousandths value 0.005

0.0000
7.6200
1.7780
0.1270

9.525

Values
from
Table 13-1

Therefore,

— inch = 9.525 mm

To use the millimeters to inches table (Table 13-2), simply look
up the value in the table. Fractions of a millimeter are not included. If
a fractional millimeter value is required, use the relationship 1 inch =
25.4 mm and calculate the value as shown in Section 13-3. For values
greater than 100 mm, look up the hundredths value in the hundredths
value table and look up the tenths and units values in the main part of
the table; then add the results to form a final equivalent value. For
example,

537 mm = how many inches?

500 mm = 19.685
37 mm = 1.457

21.142

Values
from
Table 13-2

537 mm = 21.142 inches

272

Metrics

Chap. 13

13-5 FIRST ANGLE PROJECTIONS

Not only do many foreign countries use a different measuring
standard than is used in the United States, they also use a different
projection system for presenting orthographic views. The United States
uses what is called third angle projection, but many other countries use
first angle projection. Figure 13-2 illustrates the differences in the two
systems by showing the same object drawn in each. By comparing the
two drawings shown in Figure 13-2, we see that the front views in each
system are exactly the same. The top views also appear to be the same
although they are located differently relative to the front view. If you
are familiar with third angle projections, you will know that the top
view of a first angle projection appears to be located where the bottom
view should be. This apparent reversal of locations comes about because
of the way the views are taken. In third angle projection the viewer
looks at the object. In first angle projection the viewer looks through
the object.

To clarify this concept, study the right side view of the third angle
projection and the left end view of the first angle projection. In the
third angle projection the right side view is a view taken from the right

Top

3,2

3,4

1,2

ont

Right
Side

THIRD Angle Projection

FIRST Angle Projection

Figure 13-2 A comparison between first and third angle projec-
tions of the same object.

1
I

" T ~

- T -«-

■
1

THIRD Angle Projection

FIRST Angle Projection

Figure 13-3 A comparison between first and third angle project
tions of the same object.

side of the object, looking into the object, and drawn on the same side
of the object as the viewer. In first angle projection the left end view is
a view taken from the left side of the object, looking through the ob-
ject, and drawn on the side of the object opposite the viewer. Figures
13-3 and 13-4 are two more examples that compare first and third
angle projections of the same objects. Study them. Look into and look
through the objects.

Figure 13-4 A comparison between first and third angle projec-
tions of the same object.

1 ■

THIRD Angle Projection

FIRST Angle Projection

274

Metrics

Chap. 13

From a drawing technique standpoint, the two systems are equally
demanding. Visible lines must be heavy and black. Visible lines must be
heavier than dimension lines and hidden lines. Lettering must be neat
and uniform. The projection theory presented in Chapter 4 is also
applicable, although the 45°-miter line is located differently (see Figure
13-2).

PROBLEMS

13-1 Convert the following millimeter values into inches:

a) 20 mm

b) 4 mm

c) 327 mm

d) 526 mm

e) 103 mm

f) 57 mm

g) 5384 mm
h) 910 mm
i) 38 mm

j) 237 mm

13-2 Convert the following inch values into millimeters:

a) 2.378"

b) 0.750"

c) 12.875"

d) 0.020"

e) 1.006"

f) 4.125"

g) 3.500"
h) 120.000"
i) 8.820"

j) 1.324"

13-3 Convert the following inch values into millimeters:

a) 1/2"

b) 2-1/4"

c) 3-7/8"

d) 12-5/16"

e) 5-13/32"

Your company has purchased the rights to produce some parts which
up to now have been produced only in Europe. As part of the agree-
ment, the European producer has supplied manufacturing drawings of
the parts involved. Convert these drawings, done in millimeters and first
angle projection, into drawings that may be read by American crafts-
men (decimal inches and third angle projections).

13-4

r— 25

50R

IQDIA

13-5

110

13-6

12DIA-4PLACES

34DIA

80D1A

13-7

400IA

55 *-

75 H

275

276

13-8

Metrics

Chap. 13

H 40— H

13-9

28 - 1 -

1 1*

t * 5

15 k«-
-«-30 ■*"

55 — *■
— 80

— 20

. »-

Problems

277

Your company has decided to manufacture the following parts in a
European plant. In order to do this, the manufacturing drawings must
be converted into the European system of millimeters and first angle
projections. Convert the following drawings so that they may be read
by European craftsmen:

13-10

1.00

1.75

1.00 1

\ ,38

4.00

■* 2.00 H

i J '

1.38

ir k

-75

.38

i
t
I i

13-11

278

13-12

Metrics

Chap. 13

2.00

13-13

1.63 R

1.50 DIA

1.13 Dl A

.25DRILL-.50SFACE

.53 \

-^.50

4.25 DIA

<s.

FILLETS AND ROUNDS g-R

PRODUCTION
DRAWINGS

Figure 14-0 Illustration courtesy of Teledyne Post, Des Plaines,
Illinois 60016.

14-1 INTRODUCTION

Production drawings are used to aid a craftsman in the manufac-
turing of an object. They are generally either detail drawings or assembly
drawings. A detail drawing usually presents only one object. An assem-
bly drawing presents several objects together.

It is sometimes difficult to realize that the picture portion of a
drawing is only one part of the total finished drawing. The title block,
revision block, and drawing notes are just as important as the picture
portion, and often they are just as time-consuming to prepare. This
chapter will briefly describe title blocks, revision blocks, and so on, and
will explain more specifically the makeup of detail and assembly draw-

This chapter will also present the concept of using fewer than
three orthographic views to describe an object. It will explain drawing
scales, drawing details, and several common drawing call outs.

14-2 ASSEMBLY DRAWINGS

Assembly drawings show several objects joined together. An as-
sembly drawing must include all information needed by the craftsman
to correctly assemble the parts. They do not usually include specific
object dimensions, but they do include those dimensions which are
necessary for assembly.

Figure 14-1 illustrates an assembly drawing. Each object is identi-
fied by part number, but it is not dimensioned. Hidden lines have been
omitted to make the drawing easier to read. This is not always possible,
especially for assemblies that contain internal parts.

If any specific operation is to be performed by the assembler, it
must be noted on the assembly drawing. For example, if several parts
are to be joined together by a bolt, the bolt hole should, if possible, be
drilled during the parts assembly to insure that all the parts align prop-
erly.

Assembly drawings sometimes reassign new part numbers to the
various component pieces that make up the assembly. Assembly num-
bers are usually one or two digit numbers (1, 2, 3, 14, 22, etc.) and are
added to save printing the larger, more complicated part numbers on
the assembly drawing. If assembly numbers are used, include them in a
column in the parts list next to and to the left of the part numbers.
Label the column Assy No.

280

Sec. 14-2

Assembly Drawings

281

ffl

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EC
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ac 2
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I—

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in

r-l

282

Production Drawings

Chap. 14

14-3 DETAIL DRAWINGS

Detail drawings are used by craftsmen to produce a finished object.
They are a set of instructions that should include all information neces-
sary for the complete and accurate manufacture of the object. They
should include, among other things, a complete size and shape defini-
tion of the object; the material from which the object is to be made; all
necessary information on treatment of the materials; surface finish
requirements; references to applicable company, customer, or govern-
ment specifications; any necessary inspection information; and, if
necessary, instructions for handling the finished object. Figure 14-2
illustrates a detail drawing.

MAKE FROM: 4050 CARBON STEEL

NEXT ASSY: 34762

TOLERANCES

.XX *-.01
.XXX ±003
Angular ± 1°

REVISIONS

NO | BY | CHANGjfsT

[JOB
0*644

CHAMFER WAS .31x45

NOTE

PACKAGE PER SPEC 34A

OLD AMALGAMATED

11 QUARRY TERRACE
PEABOOY.MASS 01960

on ov

■0-

CHK ,£*-

EN6 4g

DATEA-Mi

SCALEiftf

CUST

P0ST-78T442

Figure 14-2 An example of a detail drawing.

14-4 TITLE BLOCKS

The title block of a drawing contains the title of the object, the
part number, the company name and address, and signatures of the
engineers and draftsmen who prepared the drawing. It may also include
customer order numbers, tolerance specifications, signature blocks (for
various approval signatures), and the drawing scale. Figure 14-3 illus-
trates a title block.

Title blocks are usually located in the lower right-hand corner
of the drawing.

Sec. 14-6

Revision Blocks

283

TOLERANCES ON MACHINE OIMENSIONS
UNLESS OTHERWISE SPECIFIED

FRACTIONAL DIMENSIONS

- V32

ANGULAR DIMENSIONS

■ 1/2-

SURFACE FINISHES

125 V

ALL CORNERS 1/32 R OR CHAM
UNLESS OTHERWISE SPECIFIED

DRAWN

SCALE

APP'V'D

B/M

DATE

PATT.

ATWOOD & MORRILL CO.

SALEM, MASS.

Figure 14-3 A company title block courtesy of the Atwood and
Morrill Co., Salem, Mass.

14-5 PARTS LIST

A parts list is a listing of the names and numbers of parts called
out on the drawing. It may also include material information, stock
size, manufacturing quantity, finishing specifications, weight calcula-
tions, and so on. Figure 14-4 illustrates a parts list.

5QZS-0Z

CUP

.Q(>*/.$x6.C

7075-m

SQIS-O/

BRfrCKLT

2*t>*&0

STL

PART NO

QTY

DESCRIPTION

STOCK SIZE

MATL

Figure 14-4 An example of a parts list.

14-6 REVISION BLOCKS

A revision block is a listing of all changes that have been made
in the drawing. It should include a description of the change, the date
the change was made, where the change is located on the drawing, the
draftsman's initials, and any necessary approval signatures.

Revision blocks are usually located in the upper right-hand corner
of the drawing. Figure 14-5 illustrates a revision block.

Figure 14-5 An example of a revision block.

REVISIONS

CHANCE

ffATL UAS C.K3TUL

-■—

284 Production Drawings

14-7 DRAWING ZONES

Chap. 14

Large drawings are divided into zones similar to those used on a
map. Letters are used to define the horizontal zones and numbers are
used to define the vertical zones. Figure 14-6 illustrates a zoned draw-
ing.

<£<?

Figure 14-6 An example of a zoned drawing.

Zone number are usually written in boxes with the letter over the
number as follows:

C/4, D/2, A/13

etc.

14-8 DRAWING NOTES

Drawing notes are written instructions that are included as part of
a drawing. They are written because they cannot be drawn (for example,
heat treating or finishing instructions). Figure 14-1 includes a note
that defines the torquing requirements of the assembly.

14-9 ONE-, TWO-, AND PARTIAL
VIEW DRAWINGS

Up to this point we have shown three views of every object. Three
views are not always necessary for complete definition of an object and
in some cases two views are sufficient. Occasionally, just one view is
enough. Figure 14-7 is an example of a two-view drawing. Figure 14-8
is an example of a one-view drawing. In both figures the objects are
completely defined and require no other orthographic views.

Sec. 14-9

One-, Two-, and Partial View Drawings

285

±_r

A**

s«a»

Figure 14-7 An example of a two-view drawing. In this case, the
side view adds nothing to the drawing and so can be eliminated.

<$£

MAKE FROM -| CRS

Figure 14-8 An example where one view is sufficient to define
the object.

Unfortunately, there is no rule to follow in determining the num-
ber of views needed. Each object must be judged separately according
to its individual drawing requirements.

For some objects, one orthographic view and part of another are
sufficient for complete definition. A view that includes only part of an
orthographic view is called a. partial view. When and where to use partial
views is up to the discretion of the draftsman, as long as the final
drawing completely defines the object. Figure 14-9 is an example of
a drawing that includes partial views.

To show where a partial view has been broken off (the rest of the
view has been omitted), use a break line. Two kinds of break lines are
used— one for general use and one when break lines are very long.
Figure 14-10 illustrates the two break lines. Figure 14-11 presents an

286

Production Drawings

Chap. 14

Figure 14-9 An example of a drawing which includes partial
views.

BREAK LINES

for Shorter Breaks

(thick)

for Long Breaks

V —

j r

(thin)

Figure 14-10 How to draw breaklines. The wavy line used for
shorter breaks is drawn freehand whereas the line for longer breaks
is drawn as shown.

— eb ^— <+) — -<*) (+) $jh*

I — ^ ^ 1

6.74

r Y~ V 1

-<^-4> — $ — ^— § — ^- .

Figure 14-11 An example which includes a long break line.

Sec. 14-11

Drawing Scales

287

example of how the long break line is used and Figure 14-9 illustrates
the general break line. General break lines are drawn freehand as shown
in Figure 14-10.

14-10 A DRAWING DETAIL

A drawing detail is a special kind of partial drawing. It is used to
enlarge a specific part of a drawing that is too small or too complicated
to be completely understood if only shown in its existing size. Figure
14-12 is an example of a drawing that includes a drawing detail.

When you draw a drawing detail, always clearly state the scale
used and always label both the detail and the original source of the de-
tail. As with one-view, two-view, and other partial drawings, there is no
rule on when a drawing detail should be used. It is up to the draftsman
to judge his (or her) drawing and to determine whether or not a draw-
ing detail will help clarify any particular area.

SEE DETAIL A

I— -1.25-^|

— *-
.25

■

— .50

1 "

t \

■TAI

^75

SCALE 2-1

Figure 14-12 An example of a drawing detail.

14-11 DRAWING SCALES

Drawing scales are used because some objects are too big to fit on
a sheet of drawing paper and others are so small that they could not be
seen on a drawing. House drawings, for example, are drawn at a reduced
scale. Electronic microcircuits are drawn at an increased scale.

Figure 14-13 shows one full-sized and two scaled drawings of the
same square. Note that the scale used is clearly defined.

The scale note l A = 1 means that every Vfc inch on the drawing is
actually 1 inch on the object. In other words, the drawing is one-half
the size of the true object size. Similarly, the scale note 2 = 1 means

\ :

-m —

SCALE: 2-1

SCALE: 1-1

SCALE:4- = 1

. 1 _.

Figure 14-13 An example of drawing scales. The same square
has been drawn using three different scales.

that 2 inch equals 1 inch; thus, the drawing is twice as large as the actu-
al object. The note 1 = 1 means that the drawing is the exact same size
as the object.

When you dimension scaled drawings, never change the stated
dimensions. Only change the size of the picture portion of the draw-
ing. Look again at Figure 14-13. Note that the object has the same
dimensions in each scale despite the change in the drawn size of the
object.

14-12 DRILLING, REAMING,
COUNTERBORING, AND
COUNTERSINKING

Drilling, reaming, counterboring, and countersinking are very com-
mon machining operations that are called for on a drawing by a drawing
note. Each operation is defined in this section and is illustrated in
Figure 14-14.

DRILLING: a machine operation that produces holes. The bottom of
drilled holes are drawn to a 30° -tapered point as shown in Figure
14-1 4(a).

REAMING: a machine operation that smooths out the surface of a
drilled hole. From a drawing standpoint, reamings are drawn the same
way that drilled holes are drawn. The call out notes, however, are
different as shown in Figure 14-14(b).

COUNTERBORING: a machine operation in which part of a drilled
hole is redrilled to a larger diameter [see Figure 14-14(c)].
COUNTERSINKING: a machine operation in which a drilled hole is
redrilled to produce the tapered shape as shown in Figure 14-14(d).^
Countersinks are usually made at 82°, but they may be drawn at 90°
(45° on each side) as shown in Figure 14-14(d).

238

Mldsp UNO

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« a

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3"8.s
.2 S *

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"o *J *J

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££g

M»jA dox

M«jA JUOJJ

M»|A |euoi|3«s

289

290

Production Drawings

Chap. 14

PROBLEMS

14-1 Redraw the following assembly. Make any changes that you feel
will help clarify the drawing. Also draw detailed drawings of
each of the component pieces of the assembly (including the
screws). Each square on the grid is 0.20 per side.

■

14-2 Redraw the following object and add the appropriate notes.

Problem Si

291

14-3 Redraw the following object and add the following:

a) 0.44 DRILL-0.88 DEEP

b) 0.31 DIA-0.56 C BORE
0.19 DEEP

c) 0.63 DIA-82° CSK
1.38 DIA

d) 0.499-0.501 REAM

1.50

L_L

100

— 2.00 *

S75

•* 2.00

+°

2.00

+ C

+°

2.00

|—

8.00

292

Production Drawings

Chap. 14

14-4 Given the following assembly drawing, prepare detail drawings
of each of the component parts. Specify thread sizes for each of
the screws. Assume that there are six screws between the base
plate and body and six screws between the cover casting and
body. Each square on the grid pattern is 1/8 per side.

DESIGN PROBLEMS

For each of the following designs, prepare an assembly drawing and de-
tail drawings of each of the components parts, and a parts list.

14-5 Design a four-shelf bookcase.

14-6 Design a drawing table.

14-7 Design a case for carrying all your drafting equipment (do not

include drafting machines).
14-8 Prepare a detail drawing of any standard tool (hammer, wrench,

etc.).

Problems

293

14-9 Prepare an assembly drawing and detail drawings of each of the
component parts of a ball -point pen or leadh older.

14-10 Design a wine rack. Allow for bottles of at least three different
sizes.

14-11 Design a portable, removable food tray for use while eating in a
car. Specify the make of car for which you are designing the
tray.

14-12 Given the following exploded drawing of a holding fixture and
details of each of the fixture's component parts, draw a com-
plete assembly drawing of the fixture. Use whatever views
(orthographic, sectional, etc.) are necessary for complete defini-
tion of how all the pieces are to be assembled. Add a note to the
assembly drawing to have the latch pin, dowel pins, cam pivot
pin, and cover pivot pin peined after assembly. Also add a parts
list to the assembly drawing which includes a complete listing of
parts required for the assembly.

1.25

.125

Latch

.19

Holder Cam

294

14-12b

r— ,250 Dirt

Production Drawings

Chap. 14

EEE

Dowflt Pin

f£

L-.S23 OiA

2SOIA

Larfl* Buahlng

-.11 t>IA

Pin
and Cam Pivot

][

J-40 UNC-ZA

.65

.310

-d" r

1ft OIA

Small Bbahlng

Z^3-ei3--0-

I — .125 DIA Cover Pivot Pin

14-12c

3.00

.25R

Cover Plate

Problems

295

14-12d

Cover
Pivot Pin

Base Casting

14-12e

-J- 20UNC-2BX.38,
2 PLACES

jj 40UNC-2B\38

{ ^--i40UNC-2B
8 x.38 r

-25

?ii! nrtr^

■"ii w rm

•M

"i| L l 1-63

.38

.75

Base
Casting

ISOMETRIC
DRAWINGS

Figure 15-0 Photograph courtesy of Buick Division, General
Motors Corp.

15-1 INTRODUCTION

Isometric drawings are technical pictures that can be drawn by using
instruments. They are not esthetically perfect pictures because their
axes do not taper as they approach infinity. Figure 15-1 shows a
comparison between an isometric drawing of a rectangular box and a
pictorial drawing (such as an artist would draw) of the same object,
and it demonstrates the distortion inherent in isometric drawings. Note
how the back corner of the isometric appears much larger that the back
of the pictorial drawing. Despite this slight distortion, isometric draw-
ings are a valuable way to convey technical information.

Pictorial

Isometric

Figure 15-1 A comparison between an isometric drawing and a
pictorial drawing. Note the visual distortion of the top rear
comer of the isometric drawing.

The basic reference system for isometric drawings is shown in
Figure 15-2. The three lines are 120° apart and may be thought of as
a vertical line and two lines 30° to the horizontal, which means that
they may be drawn by using a 30-60-90 triangle supported by a T-
square. All isometric drawings are based on this axis system.

Normally, an isometric drawing is positioned so that the front,
top, and right side views appear as shown in Figure 15-3. This may be

297

Figure 15-2 The basic reference system for isometric drawings.

Fiffure 15-3 Definition of the relationship between the front,
top? and side views as drawn orthographical and isometncally.

varied according to the position that the draftsman feels best shows

the object. . ,

Dimensional values are transferable from orthographic views only
to the axis, or lines parallel to the axis, of isometric drawings. Angles
and inclined dimensional values are not directly transferable and require
special supplementary layouts which will be explained in this chapter.

298

Sec. 15-2

Normal Surfaces

299

Isometric drawings do not normally include hidden lines, although
hidden lines may be drawn if special emphasis of a hidden surface is
required.

15-2 NORMAL SURFACES

Figure 15-4 is a sample problem that requires you to create an
isometric drawing from given orthographic views. Since all surfaces in
the problem are normal (90° to each other), all dimensional values may
be transferred directly from the orthographic views to the isometric
axis, or lines parallel to the isometric axis. The basic height, width, and
length of the object are VA, 2, and 3, respectively, in both the isometric

GIVEN: Front, top and side views.
PROBLEM: Draw an isometric drawing.

Figure 15-4

and orthographic drawings. Figure 15-5 is the solution to Figure 15-4
and was derived by the following procedure:

SOLUTION:

1. Make, to the best of your ability, a freehand sketch of the solu-
tion. See Section 5-6 for instructions on how to make sketches.
Remember that since it is easier to make corrections and changes
on a sketch than on a drawing, you should make your sketch
as complete and accurate as possible.

Figure 15-5(a)

300

Isometric Drawings

Chap. 1 5

Using very light lines, lay out a rectangular box whose height,
width, and length correspond to the height, width, and length
given in the orthographic views.

Figure 15-5(b)

3. Using very light lines, lay out the specific shape of the object.
Transfer dimensional values directly from the orthographic
views to the axis, or lines parallel to the axis, of the isometric
drawing.

Figure 15-5(c)

Figure 15-5{d)

4. Erase all excess lines and smudges; carefully check your work;
and then darken in all final lines to their proper color and pat-
tern.

Figure 15-5(e)

Sec. 15-2

Normal Surfaces

301

Figure 15-6 is another example of an isometric drawing created
from given orthographic views and including only normal surfaces.

GIVEN: Front, top, and side views.
PROBLEM: Draw an isometric drawing.

SOLUTION:

1
_ J

1 —

1
_J

Figure 15-6(a)

Figure 15-6(b)

Figure 15 -6(c)

Figure 15 -6(d)

Figure 15-6(e)

Figure 15-6{fj

Figure 15 -6(g)

302

Isometric Drawings

Chap. 15

GIVEN: Front, top, and side views.
PROBLEM: Draw an isometric drawing.

15-3 SLANTED AND OBLIQUE
SURFACES

Figure 15-7 is a sample problem that involves the creation of an
isometric drawing from given orthographic views that contain a slanted
surface. The slanted surface is dimensioned by using an angular dimen-
sion that presents a problem because angular dimensions cannot be
directly transferred from orthographic views to isometric drawings.

Figure 15-7

To transfer an angular dimensional view from an orthographic
view to an isometric drawing, convert the angular dimensional value to
its component linear value and transfer the component values directly
to the axis of the isometric drawing. Figure 15-8 illustrates this pro-
cedure by showing two angular dimensions that have been converted

Figure 15-8 Two examples of angular di-
mensions which have been redimensioned
using their linear coordinates. The linear
coordinates have been transferred to an iso-
metric axis.

Sec. 15-3

Slanted and Oblique Surfaces

303

to their respective component linear values and then showing how these
values are transferred to the isometric axis. Normally, a draftsman
simply measures his' full-sized orthographic views and then transfers the
information, but if this information is not available, he (or she) makes a
supplementary layout from which the necessary values may be measured.
Supplementary layouts may be made on any extra available paper and
should be saved for reference during the checking of the drawing.

Figure 15-9 is the solution to Figure 15-7 and was derived by the
following procedure:

SOLUTION:

1. Make, to the best of your ability, a freehand sketch of the solu-
tion.

..v

Figure 15-9 (a)

2. Using very light lines, lay out a rectangular box whose height,
width, and length correspond to the height, width, and length
given in the orthographic views.

Figure 15-9(b)

304

Isometric Drawings

Chap. 15

3. Using very light lines, lay out the specific details of the object.
Where necessary, make supplementary layouts that furnish the
linear component values which you can transfer to the isomet-
ric axis. In this case, the 30° component layout is shown in
Figure 15-8.

Figure 15-9(c)

Figure 15-9(d)

Figure 15-9(e)

4. Erase all excess lines and smudges; check your work; and then
draw in all lines to their proper color and pattern.

Figure 15-9(f)

Sec. 15-3

Slanted and Oblique Surfaces

305

Figure 15-10 is a sample problem that requires you to make an
isometric drawing from given orthographic views that include an oblique
surface. The solution was derived by using basically the same procedure
that was used for slanted surfaces. As with angular dimensional values,
the dimensional values that define an oblique surface must be converted
to their respective linear component values before they may be trans-
ferred to the isometric axis. If necessary, supplementary layouts should
be made. Figure 15-11 is the solution to Figure 15-10.

GIVEN: Front, top, and side views.
PROBLEM: Draw an isometric drawing.

Figure 15-10

SOLUTION:

Figure 15-1 1(a)

Figure 15-1 1(e)

306

Isometric Drawings

Chap. 15

15-4 HOLES IN ISOMETRIC DRAWINGS

There are two basic methods for drawing holes for isometric draw-
ings One method is to use instruments and draw the holes by using the
four-center ellipse method. The other method is to use an isometric
hole template as a guide. The template is much easier and faster to use,
but templates are available only in standard hole sizes. Very large or
odd-sized holes may only be drawn by using the four-center ellipse

method- *«-•#*%

The four-center ellipse method is presented in Figure 15-14(a).
When you use this method, be careful that the four centers are located
accurately. If the centers are not located properly, the four individual
arcs will not meet to form a smooth, continuous ellipse. A good prac-
tice that will help you draw a smooth continuous ellipse is to lightly
construct the ellipse and then check it for accuracy before drawing in

the final heavy arcs.

An isometric hole template may be conveniently used as a guide
for drawing the hole size for which it is cut. Figure 15-12(a) illustrates
an isometric hole template. To align the template for drawing, first
draw in the hole center lines, and then align the guidelines printed on
the template adjacent to the desired hole with the center lines on the
drawing. If you are still unsure of how to position the template, draw
in the center lines and the major and minor axes of the ellipse as shown
in Figure 15-12(b). Then align the template with the four intersections
formed by the center lines as they cross the major and minor axes
(labeled points 1, 2, 3, and 4 in Figure 15-12) and draw in the ellipse.

MU»

Figure 15-12(a) Isometric hole template

Figure 15-1 2(b)

Sec. 15-4

Holes in Isometric Drawings

307

GIVEN: Front and side views.
PROBLEM: Draw an isometric drawing.

-■

Figure 15-13

Figure 15-13 is a problem that requires you to draw a hole in an
isometric drawing. Figure 15-14 is the solution using the four-center
ellipse method, and Figure 15-15 is the solution using an isometric hole
template.

Figure 15-1 4 (a) Four center method for drawing isometric elip-
ses. Note: this method is ONLY good for isometric drawings; use
the approximate elipse method described in Section 3-28 for all
other elipses.

Indicates the location of compass center points

308

Isometric Drawings

Chap. 15

SOLUTION:

Figure 15-14(b)

Figure 15-14(d)

Figure 15-1 4(c)

Figure 15-14(e)

Figure 15-14(f)

Holes in Isometric Drawings

Figure 15-1 5(e)

310

Isometric Drawings

Chap. 15

Figure 15-16 When does the bottom edge
of a hole show in an isometric drawing?

In drawing a hole for an isometric drawing there arises the ques-
tion of whether or not the bottom edge of the hole can be seen. If it
can be seen, how much of it can be seen? Figure 15-16 illustrates the

problem.

To determine exactly if and how much of the bottom edge of the
hole should be drawn, locate the center point of the hole on the bot-
tom surface and draw in the hole by using the same procedure you used
for the hole on the top surface. If the hole drawn on the bottom sur-
face appears within the hole on the top surface, it should appear on the
finished drawing. If the hole drawn on the bottom surface does not ap-
pear within the hole on the top surface, it should not appear on the
finished drawing. Figure 15-17 presents a sample problem that illus-
trates this procedure.

GIVEN: A front view.

PROBLEM: Draw an isometric drawing.

Figure 15 -17 (a)

Figure 15-1 7(b)

Figure 15-1 7(c)

Cantarpoinl for
Bottom Surfaca

Figure 15-1 7(d)

Figure 15-17(e)

Sec. 15-5

Round and Irregular Surfaces

311

15-5 ROUND AND IRREGULAR
SURFACES

Figure 15-18 is a sample problem that requires you to create an
isometric drawing from given orthographic views that contain a round
surface. To make an isometric drawing of a round surface, use either an
isometric template for a guide or the point method as described in this
section. Figure 15-19 is a solution to Figure 15-18 that was derived by
using an isometric ellipse template. Figure 15-20 is a solution that was

GIVEN: Front, top, and side views.
PROBLEM: Draw an isometric drawing.

SOLUTION:

Figure 15-1 9(a)

i r

Figure 15-18

Figure 15-19(b)

Figure 15-19(c)

Figure 15-19(d)

Figure 15-19(e)

Figure 15-19(f)

Figure 15-I9(g)

312

Isometric Drawings

Chap. 15

SOLUTION:

AJ-

PH«

Figure 15-20(a)

Figure 15-20(b)

Figure 15-20(d)

Figure 15-20(e)

Figure 15-20(f)

Figure 15-20(g)

derived by using the point method. The procedures are as Allows To
draw a round surface by using an isometric ellipse template, do the fol-

lowing:

1 Define on one of the orthographic views (the one that shows
' the round surface as part of a circle) the center point of the

Sec. 15-5 Round and Irregular Surfaces 313

round surface and the intersections of the center lines with the
surfaces of the object. In this example the center point is
marked 0, and the two intersections are marked points 1 and 2.

2. Draw a rectangular box and transfer the points 1, 2, and to
the front plane of the isometric drawing and label them 3, 4,
and 5.

3. Project the points in the front plane across the isometric draw-
ing to the back Diane.

4. Align the proper hole in the isometric ellipse template with the
center lines on the front isometric surface, and draw in the iso-
metric arc. Repeat the same procedure for the back surface.

5. Erase all excess lines and smudges; check your work; draw in
the remaining lines of the object lightly at first and then darken
them to their proper color and pattern.

To draw a round surface by using the point method; do the following:

1. On one of the orthographic views (the one that shows the round
surface as part of a circle) mark off a series of points along the
rounded surface. The points need not be equidistant. The more
points you take, the more accurate will be the final isometric
ellipse. If necessary, make a full-sized supplementary layout.

2. Dimension each point horizontally and vertically as shown.

3. Transfer the dimensional values to the isometric axis as shown.

4. Using a French curve as a guide, draw in the isometric arc.

5. Transfer the points to the back of the surface, and, again using
a French curve as a guide, draw in the isometric arc.

6. Erase all excess lines and smudges; check your work; draw in
the remaining lines of the object lightly at first and then darken
them to their final color and pattern.

Figure 15-21 is a sample problem that requires you to draw an iso-
metric drawing from given orthographic views that contain an irregular
surface. The point method described for drawing isometric drawings of
round surfaces is directly applicable to the creation of isometric draw-
ings of irregular surfaces provided that we use two of the orthographic
views to locate the points. Two views are required because the surface
may not be parallel to any of the principal planes. Figure 15-22 is the
solution to Figure 15-21.

GIVEN: An object.

PROBLEM: Draw an isometric drawing of the object.

MATL -J C.R. STEEL

Figure 15-21

Isometric Drawings

Figure 15-22(b)

Figure 15-2 2(d)

Chap. 15

Figure 15-22(a)

Figure 15-22(c)

Figure 15 -2 2(e)

Sec. 15-6

Isometric Dimensions

315

15-6 ISOMETRIC DIMENSIONS

Isometric drawings may be dimensioned by using either the aligned
system or the unidirectional system. All isometric drawings in this book
are dimensioned by using the unidirectional system. Section 6-4 gives a
further explanation of the differences between the two systems.

Regardless of the system used, the leader lines must be drawn in
the same isometric plane as the surface they are defining. The guide-
lines for the dimensions in the aligned system are drawn parallel to the
edge being defined while the guidelines for the unidirectional system
are always horizontal. Figure 15-23 is another example of the unidirec-
tional system. The numbers are drawn 1/8 to 3/16 in both systems.

-75 -2 PLACES

.62 DIA

.33 DIA

Figure 15-23 An example of an isometric drawing dimensioned
using the unidirectional system.

15-7 ISOMETRIC SECTIONAL VIEWS

Isometric sectional views are used for the same reasons that ortho-
graphic sectional views are used— to clarify objects by exposing impor-
tant internal surfaces that would otherwise be hidden from direct view.
Figure 15-24 shows a full isometric sectional view and a half isometric
sectional view. Note that, as with orthographic sectional views, hidden
lines are omitted and the cross-hatching lines are drawn medium to

Figure 15-24 Isometric section cut.

316

Isometric Drawings

Chap. 15

light in color, 3/32 apart at an inclined angle. Isometric sectional views
do not require a defining cutting plane and are usually presented as
individual pictures with no accompanying reference drawing. Dimen-
sions are placed on an isometric sectional view in the same way they
are for regular isometric drawings.

15-8 AXONOMETRIC DRAWINGS

Isometric drawings are actually just one of a broad category of
drawings called axonometric drawings. An axonometnc drawing is a
pictorial drawing, drawn with instruments, that uses some initially
defined axis system which remains parallel to infinity.

There are three kinds of axonometric drawings: isometric, di-
metric, and trimetric. The classification of an axonometric drawing
depends on its axis system. An isometric axis has three equal angles
f 120° ) a dimetric axis has two equal angles, and a trimetric axis has no
equal angles. Figure 15-25 shows examples of the three axonometric
axes. The oblique drawing, which is covered in the next chapter, is a
special form of trimetric drawing.

Dimetric

Trimetric

Figure 15-25 Examples of the three different types of axono-
metric drawings: isometric, dimetric, and trimetric.

Figure 15-26 An adjustable triangle.

An adjustable triangle, such as the one shown in Figure 15-26, is
useful when you are creating axonometric drawings because it may be
set to any angle, thereby eliminating the need for constant measuring
with a protractor.

15-9 EXPLODED DRAWINGS

Figure 15-27 is an example of an exploded drawing. Exploded
drawings are useful because they enable the reader to visualize and
understand technical information without requiring him (or her) to
have a knowledge of orthographic projections. They are particularly
well-suited to assembly drawings because they easily show the relation-
ship between the various parts.

Figure 15-27 An exploded drawing.

317

318

Isometric Drawings

Chap. 15

Exploded drawings may be drawn by using any one of the axono-
metric axis systems provided that the system chosen helps present the
information clearly. Exploded drawings rarely contain dimensions or
hidden lines because they are usually intended more to be pictures of
technical information than actual technical drawings. Parts in an ex-
ploded drawing are always labeled either by name or by part number.

PROBLEMS

Create isometric drawings of the following objects. Dimetric and trimet-
ric drawings may also be created if assigned by your instructor.

15-1

r*i

-J *1-

- * '

15-2

JJ-

ffl

±t

15-3

3.00

1.50

1.00

i 2.25

1.50

! '

^.75

15-4

§£

1 '•

- I.UU

! i :

^,50

15-5

^>;

319

320

15-15

Isometric Drawings

Chap. 15

75DIA

2.00

15-16 Draw an exploded isometric drawing of the following assembly.
The washers are 1.00 O.D., 0.50 I.D., and 0.06 thick. Figure
PI 5-1 6(a) illustrates how to draw an isometric representation of
a bolt.

WASHER
2 REQD
.063X.75 O.D.
x.44 I.D.

SPACER
.25THK

-|-16UNC-2AX1-|

447ST67
.63THK

EEJ ^ NUT

Problems

321

15-17

4.00

I— .*5

-.25 DIA
4 PLACES

i i

3.50

1.7$

■1.00

Obfsct is symmetrical
about both axis

322

15-6

Isometric Drawings

2.50

1.50

v ,f

L .75

Chap. IS

K03

T,3

138

15-7

.88 R

15-8

„.

I?.

—

Problems

323

15-9

3.58

15-11

1.13R J5.X0

94 R

3ff\

2.38

60°

15-12

Sill

15-13

j—

•— :25

1.25

...

Object is symmetrical
about both
center lines

\--„ 4-, J

\ \ fi.

1- -r _ ^ J _

,38

: :: 1

1.38

^.88
—68

OBLIQUE DRAWINGS

Figure 16-0 Photograph courtesy of AMF/Harley-Davidson.

16-1 INTRODUCTION

Oblique drawings are technical pictures that can be drawn with
instruments. They are easier to draw than isometric drawings, but they
contain more inherent visual distortion. Figure 16-1 compares oblique,
isometric, and pictorial drawings of the same object and illustrates the
visual difference among the three drawings.

The basic reference system for oblique drawings is shown in Fig-
ure 16-2. The most distinct characteristic of the oblique axis is the
90° relationship between the left-hand axis .and the vertical axis. Be-
cause of this 90° relationship, the front view and all surfaces parallel to
it are almost identical to the front view of an orthographic drawing.
This makes it very easy to transfer information between the two dif-
ferent front views.

Figure 16-1 A comparison between an isometric, a pictorial, and
an oblique drawing. Note the amount of visual distortion in each.

Pictorial

Isometric

Oblique

Any Angle

Figure 16-2

325

326

Oblique Drawings

Chap. 16

The receding lines may be drawn at any convenient angle. (Up-
ward and to the right at either 30° or 45° is most commonly used
because these angles may be drawn with standard triangles.) The choice
of which receding angle to use depends on which angle best shows the

object involved. .

Dimensional values are directly transferable from the front view
of the orthographic drawing to the front view of the oblique drawing.
Circles transfer as circles, not as ellipses as in isometric drawings, and
angles transfer as the same angles. Dimensional values in all other views
are not directly transferable. They can only be transferred from the
orthographic views to the receding axis of the oblique drawing.

Sometimes when dimensional values are transferred to the receding
axis of the oblique drawing, they are redrawn at a reduced scale The
scale reduction improves the visual quality of the drawing. Note that in
Figure 16-3 the reduced scale of the receding axis changes the way the
object looks. Although any scale reduction may be used, the most
common is the half-scale reduction called a cabinet projection. If the
dimensional values are transferred full scale, the resulting oblique draw-
ing is called a cavalier projection.

Oblique drawings do not normally include hidden lines, although
they may be used if special emphasis is required.

Scale

Cavalier
Projection

Z7\

/—A

-i- Scale

Scale

Cabinet

Projection

Figure 16-3 A comparison between different scaled receding
lines on oblique drawings. Note the difference in visual distortion
in each.

Sec. 16-2

Normal Surfaces

327

16-2 NORMAL SURFACES

Figure 16-4 is a sample problem that involves creating an oblique
drawing from given orthographic views. Since all surfaces in the problem
are normal (at 90° to each other), all dimensional values may be di-
rectly transferred from the orthographic views to the axis of the oblique
drawing. All values are to be transferred at full value, which means that

GIVEN: Front, top, and side views.
PROBLEM: Draw an oblique drawing.

-« L

-« W

Figure 16-4

the resulting oblique drawing is a cavalier projection. Figure 16-5 is the
solution to Figure 16-4 and was derived by using the following pro-
cedure:

SOLUTION:

1. Make, to the best of your ability, an oblique freehand sketch of
the proposed solution.

JS ^

Figure 16-5(a)

328

Oblique Drawings

Chap. 16

2. Using very light lines, lay out a rectangular box whose height,
width, and length correspond to the height, width, and length
given in the orthographic views. In this case, a receding axis of
30° was chosen.

Figure 16-5(b)

3. Using very light lines, lay out the specific details of the object.
Transfer the dimensional values directly from the orthographic
views to the axis of the oblique drawing. For example, use a
pair of dividers and verify all other dimensional values.

Figure 16-5(c)

Figure 16-5(d)

Erase all excess lines and smudges; check your work; and draw
in all lines to their final color and configuration.

Figure 16-5(e)

Sec. 16-2

Normal Surfaces

329

Figures 16-6, 16-7, and 16-8 are further examples of oblique
drawings created from given orthographic views.

GIVEN: Front, top, and side views.
PROBLEM: Draw an oblique drawing.

-* W *

SOLUTION:

Figure 16 -6(b)

Figure 16 -6(g)

330

Oblique Drawings

Chap. 16

GIVEN: Front, top and side views.
PROBLEM: Draw a cabinet oblique drawing.

SOLUTION:

Figure 16 -7 (a)

■

Figure 16-7(b)

Figure 16-7(c)

Half Scale

,«

?•"

*£=*

*£

Figure 16-7(d)

Figure 16-7(e)

Figure 16-7(f)

Cabinet Projection

Figure 16-7(g)

Sec. 16-2

Normal Surfaces

331

GIVEN: Front, top, and side views.

PROBLEM : Draw an oblique drawing with the receding axis slanted

45° to the left.

SOLUTION:

Figure 16-8(a)

Figure 16-8(b)

Figure l6-8(c)

Figure 16-8(d)

Figure 16-8(e)

Figure 16-8(f)

Figure 16-8(g)

332

Oblique Drawings

Chap. 16

16-3 INCLINED AND OBLIQUE
SURFACES

Figure 16-9 is a sample problem that involves creating an oblique
drawing from given orthographic views that contain an inclined surface.
Unlike isometric drawings, angular dimensions may be directly trans-
ferred from the front orthographic view to the front oblique view, there-
by eliminating the need for supplementary layouts. Remember that
this direct transfer only works on the front views and on surfaces
parallel to the front view.

GIVEN: Front, top, and side views.
PROBLEM: Draw a cabinet oblique drawing.

f ■

i
i

Figure 16-9

SOLUTION:

Figure 16-10 is the solution to Figure 16-9 and was derived by
using the same procedure presented for normal surfaces in Section 16-2.

Figure 16-10(a)

HALF SCALE

Figure 16-10(b)

Sec. 16-3

Inclined and Oblique Surfaces

333

Figure 16-10(d)

Figure 16-1 0(e)

Figure 16-1 0(f)

Figure 16-11 is a sample problem that involves an object that in-
cludes an oblique surface. The angle must be broken down into its
linear components, and then the linear components may be transferred
to the axis of the oblique drawing. Figure 16-12 is the solution to
Figure 16-11 and was derived by using the same procedure outlined
for Figure 16-4 in Section 16-2.

GIVEN: Front, top, and side views.
PROBLEM: Draw an oblique drawing.

Figure 16-11

334

Oblique Drawings

Chap. 16

SOLUTION

Figure 16-12(a)

Figure 16-1 2(b)

Figure 16-12(c)

Figure 16-1 2(d)

Figure 16-1 2(e)

Figure 16-1 2(f)

Figure 16-1 2(g)

Sec. 16-4

Holes in Oblique Drawings

335

16-4 HOLES IN OBLIQUE DRAWINGS

The techniques required to draw holes in oblique drawings vary
according to the surface on which you are working. On the front sur-
face and on all surfaces parallel to the front surface, holes are per-
fectly round and may be drawn with the aid of a compass or a circle
template. On any other surface elliptical holes must be drawn. Ellipti-
cal holes may be drawn by using either the four-center ellipse method
or by using an elliptical template as a guide. Remember that when you
use an elliptical template, use only a template cut to the correct hole
size, at the correct angle, which has been correctly aligned to the el-
liptical hole's center line.

When you are creating oblique drawings, take advantage, if possible,
of the unique characteristics of the front view by positioning the ob-
ject with as many holes as possible located in the front view. Figure
16-13 shows two oblique drawings of the same object and demonstrates
the value of correct object positioning. In the drawing on the left the
object is positioned so that all holes are located in the front view; in
the drawing on the right the object is positioned so that the holes are
located in one of the receding surfaces. This difference is positioning
enables the left drawing to be drawn by using circles for holes; the
right drawing requires elliptical holes. Because of the elliptical hole
requirement, the drawing on the right takes about four times as long to
draw as the drawing on the left. In addition, there is no appreciable
gain in technical clarity. It is, however, important to remember that in
positioning an object your first consideration should be technical
clarity and ease of understanding for the reader and not ease of draw-
ing for the draftsman.

6>T

Poorly

Positioned

Correctly
Positioned

Figure 16-13 Two oblique drawings of the same object, one cor-
rectly positioned and pne poorly posibioned.

336

Oblique Drawings

Chap. 16

16-5 ROUNDED AND IRREGULAR
SURFACES

Figure 16-14 is a sample problem that involves creating an oblique
drawing from given orthographic views that contain a rounded surface.

GIVEN: Front and side views.
PROBLEM: Draw an oblique drawing.

Figure 16-14

Figure 16-15 is the solution and was derived by using the following
precedure:

SOLUTION:

1. Make, to the best of your ability, an oblique freehand sketch of
the solution.

Figure 16-1 5(a)

Sec. 1 6-5

Rounded and Irregular Surfaces

337

2. Using very light lines, lay out a rectangular box whose height,
width, and length correspond to the height, width, and length
given in the orthographic views.' In this example a basic cylinder
shape was substituted for the rectangular shape used.

Figure 16-1 5(b)

Figure 16-1 5(c)

Figure 16-1 5(d)

3. Using very light lines, lay out the specific details of the object.
In this example the round portions of the object are all posi-
tioned so that they appear in the front view or in views parallel
to the front view. This positioning makes the object easier to
draw.

Figure 16-15(e)

4. Erase all excess lines and smudges, and draw in all lines to their
final color and configuration-

Figure 16-1 5(g)

338

Oblique Drawings

Chap. 16

Figure 16-16 is another example of a rounded surface problem.

Figure 16-17 is a sample problem that involves creating an oblique
drawing from given orthographic views that contain an irregular surface.
Figure 16-18 is the solution and was derived by breaking down the ir-
regular surface into its defining points, locating these points in terms of
the oblique axis system, transferring the points to the oblique drawing,
and then reconnecting the points to form the oblique drawing of the
irregular surface. The remainder of the oblique drawing is created as
previously described. Figure 16-19 is the supplementary layout that
was used to locate the irregular surface in terms of the oblique axis
system.

GIVEN: Front view and material thickness.
PROBLEM: Draw an oblique drawing.

SOLUTION:

MATL

2.00 AL6064-T4

Figure 16-1 6(a)

Figure 16-16(b)

Figure 16-16(c)

Figure 16-1 6(d)

Figure 16-16(e)

GIVEN: Front view and material thick-
ness.
PROBLEM: Draw an oblique drawing.

MATL
.75 THK

Figure 16-17

Sec. 16-5
SOLUTION:

Rounded and Irregular Surfaces

339

Figure 16-1 8(a)

^-'

Figure 16-18(b)

Figure 16-18(c)

*t— (-

Figure 16-18(d)

Figure 16-18(e)

Figure 16-18(f)

16-6

Figure 16-19 Supplementary layout used to define the irregular
surface in terms of its linear components.

DIMENSIONING AN OBLIQUE
DRAWING

Oblique drawings may be dimensioned by using either the unidirec-
tional or aligned systems. The front view and all other surfaces parallel
to it are dimensioned in the same way that they were in the orthographic
views (see Chapter 6), but dimensions along the receding axis must be
drawn in the same oblique plane as the surface they are defining.

In the aligned system, guidelines for dimensions that define re-
ceding surfaces must be drawn parallel to the receding axis. Guidelines
for dimensions that define surfaces in the front view or any surface
parallel to the front view are drawn either horizontally or vertically
depending on whether they are defining horizontal or vertical surfaces.

In the unidirectional system, all guidelines are drawn horizontally.
In both systems, all letters and numbers are drawn either 1/8 or 3/16 in

height.

Figure 16-20 is an example of an oblique drawing that has been
dimensioned by using the unidirectional system.

Figure 16-20 An example of an oblique drawing which has been
dimensioned using the unidirectional system.

1.00R-4 PLACES

; 594 DIA-4 PLACES

340

Problems

341

16-7 OBLIQUE SECTIONAL VIEWS

Figure 16-21 illustrates a full oblique sectional view, and Figure 16-
22 illustrates a half oblique sectional view. Oblique sectional views are
drawn in the same manner and for the same reasons that isometric sec-
tional views are drawn. Since the only difference between the two
sectional views is the defining axis system, the information given in Sec-
tion 15-7 may also be applied to oblique sectional views.

Figure 16-21 A full oblique section cut.

Figure 16-22 A half oblique section cut.

PROBLEMS

Create oblique drawings of the following objects. Each square on the
grid background is 0.20 p.

16-1

1.25

-i -ll

1.75

l,lt*

Oi5

I 1.50

T .

.50 ,

' Y

L-.75

2.50

16-4

342

16-2

Oblique Drawings

Chap. 16

[iiniinnmn iiiiiiiiiM

■ H

_ _, — — — — — - —

L .

.„___.------ „„-___

I [ M|M||MJM

16-3 All dimensions are in millimeters.
100 DIA

30DIA

16-5

1.25 DIA

1.50 8

*—

h—

15 H-

-*\ .63 h«-

L-1.38— |

Problems

343

16-6

16-7

16-8

2.75 DIA

.88 DIA

2.25 DIA

•i

- H

.63

.13-^

■M-

UrL

1.25

1.25
DIA

3.25
DIA

38^

SYM

344

Oblique Drawings

Chap. 16

16-9

16-10

1.25DIA

.50DIA
4 PLACES

50TYP

5.00 Dl A

3.00 Dl A

3.75 Dl A

16-11

MATL.25 STEEL

Problems

345

16-12

.50 DIA

.25 DIA
4 PLACES

1.00

dto^

» I i J I :

2.25

4.00

MATL
4- THK

.88

16-13

1.00

16-14

1 1 1 1 J W--

Ml 1

-.*_ it

--i-

?27

__.._

Z/2

: Jt — s v

a ^\T

t \

A --_

~» ~ ^ "

V i h ~

—Z.1~

H V ./ t

— ■*-»-, WJ

^i ttt

*Z2,

7z/^ r7 :

f XJ* z^

uul£2jn^

™ I :

,-hh

-J r -20UNC-2Axii
HEX HEAD

WASHER
063X.75QD.X.38I.D.

COVER .38THK

BASE .63 THK

NUT

16-15

3,00

346

16-16

Oblique Drawings

Chap. 16

.38

-75

75 R

DEVELOPMENT
DRAWINGS

jHnC'i;

Figure 17-0 Photograph courtesy of General Motors Corp.

GIVEN: An object.

PROBLEM: Develop the flat pattern.

Figure 17-1

SOLUTION:

1,4 2£

Figure 17-2(a)

17-1 INTRODUCTION

Development drawings are flat patterns which, when folded in an ap-
propriate manner, form a desired object. They are most commonly used

in sheet metal work.

There are four major categories of development drawings: prisms,
cylinders, pyramids, and cones. Prism and cylinder development draw-
ings are created by using the same basic drawing techniques. Pyramid
and cone development drawings also use the same basic drawing tech-
nique. This chapter will explain and present solved sample problems of

each category.

When you make actual patterns, your development drawing will
usually include extra metal for bend and seam allowances. The amount
of extra metal to be included depends on the kind of metal being fab-
ricated, the thickness of the metal, and the kind of seam to be used.
This chapter does not include information on bend or seam allowance;
it presents only the information required to develop a given object into
its ideal flat pattern.

17-2 RECTANGULAR PRISMS

Figure 17-1 is an example of a problem that involves a rectangular
prism All surfaces are 90 c to each other. The problem is to develop a
flat pattern which, when folded properly, will form the desired rectan-
gular prism. Assume that the object is completely enclosed and that
there are no open surfaces. Figure 17-2 is the solution and was derived
by the following procedure:

1. Draw as many orthographic views as are necessary to completely
define every surface of the given object. In this example two
views (front and top) are sufficient, but for most objects more
than two views are needed. Partial orthographic views, including
auxiliary views are sometimes used to insure a complete defim-

- tion of surfaces not clearly defined in the given orthographic

views.

Position the orthographic views on the left side of the drawing

paper.
2 Define all points of the object. Use numbers for the points
' along the bottom edges and letters for the points along the top

edges. This identification system will prevent confusion as you

develop the surfaces.
3. From the front orthographic view, extend a very light layout

line from every labeled point as shown in Figure 17-2(c). All

of these lines should be parallel to each other. These lines are

called stretchout lines.

348

1.4

2,3

B
2

B,C

Figure 17-2(b)

1 2 " ~ J

Figure 17 -2(c)

1,4

2,3

Figure 17 -2(d)

349

350

Development Drawings

Chap. 17

Somewhere along the bottom (lowest) stretchout line, define
point 1. Then, using point 1 as a starting mark, lay out (along
the bottom stretchout line) the remaining points that define the
bottom edges of the object. This may be done by transferring
the line distances found in the orthographic views. Label each
point as you mark it off. There should be two point Is along
the stretchout line because the object must end at the same
point at which it started in order for the object to be completely
enclosed. Remember that line 4-1 is also part of the object.
Draw lines, perpendicular to the stretchout lines, from each
point located on the stretchout line.

2,3

1 5

3 1

Figure 17 -2(e)

6. Identify and label all points originally defined in the ortho-
graphic views on the flat pattern portion of the drawing by
using the stretchout lines drawn in step 3 and the perpendicular
lines drawn in step 5. For example, point A is known (from the
information found in drawing the orthographic views) to be
located directly above point 1. We also know that point A is
somewhere along the stretchout line drawn from point A in
step 3. Where the point A stretchout line intersects the perpen-
dicular line from point 1 is point A in the flat pattern. Point A
could also have been found by directly transferring the distance
A-l from the front orthographic view to the line perpendicular
to point 1 on the stretchout line,

7. Lay out the top and bottom of the object as shown in Figure
17-2(d). This can be done by either transferring the distance
and angles from the orthographic views or by drawing lines
perpendicular to lines C-D and 3-4 located on the flat pattern

!7j .

Sec. 1 7-2

Rectangular Prisms

351

and then, using a compass, drawing arcs of lengths B-C, D-A,
2-3, and 4-1 from points C, D, 3, and 4, respectively. The
compass method was used in this example.
8. Erase all excess layout lines. Darken in the outside periphery of
the flat pattern with heavy visible lines. Do not erase the layout
lines that represent the lines along which the pattern is to be
folded. The point labels may or may not be erased, depending
on the individual shop requirements.

Figure 17-3 is another example of a problem that involves a rect-
angular prism. Figure 17-4 is the appropriate development drawing and
was derived by using the same procedure outlined for Figure 17-2. Note
how the top surfaces were developed in this example.

SOLUTION:

GIVEN: An object.

PROBLEM: Develop the flat pattern.

Figure 17-3

I kj ih g

a b|c die f
1 2

e,h

1,4 23

Figure 17 -4(a)

ikii nfi"u

3 P\ c die ,f
1 2

fej d,«

* k Li*

2,3

1 2

Figure 17 -4(b)

nzr \

1 2

h g

qi 4i

3,l

1,9

e.h

1 2

Figure I7~4(c)

352

Development Drawings

Chap. 17

4, , , 3

1 klj ilh g

j <

c d

h 9

£U

cid

Figure 17 -4(e)

17-3 INCLINED PRISMS

prism

Figure 17-5 is an example of a problem that involves an inclined
. In this example a supplementary partial auxiliary view was needed

4 addition to the two standard views (front and top) to completely
define the inclined surface. Figure 17-6 is the development drawing for
the object shown in Figure 17-5 and was derived by using basically the
same procedure that was outlined for Figure 17-2. Note that in the flat
pattern portion of the development drawing the four corners of the in-
clined surface are 90°.

Sec. 1 7-3

Inclined Prisms

353

GIVEN: An object.

PROBLEM: Develop the flat pattern.

SOLUTION:

Figure 17-5

2 3

Figure 17-6{b)

Figure 17 -6(a)

4 1

TRUE SHAPE of
PLANE v-w-x-y

w s_

2 3

Figure 17-6(c)

4 1

Figure 17 -6(d)

z u

Figure 17-6(e)

17-4 OBLIQUE PRISMS

Figure 17-7 is an example of a problem that involves an oblique
prism, that is, a prism that contains an oblique surface 1-2-3. In order
to develop a correct flat pattern, you must know the exact shape of
surface 1-2-3. To find the exact shape of surface 1-2-3, draw a second-
ary auxiliary view. The true shape of surface 1-2-3, once completely
defined, may be transferred to the flat pattern. Figure 17-8 is the devel-
opment drawing for Figure 17-7 and is derived by using basically the
same method outlined for Figure 17-2. Figure 17-9 is the solution to
this problem.

354

Sec. 174

Oblique Prisms

355

GIVEN: An object.

PROBLEM: Develop the flat pattern.

SOLUTION:

Figure 17-7

4 1

5 , 4 1

True Shape
of Plane 1-2-3

Figure 17-8 A supplementary layout used to
determine the true shape of surface 1-2-3.

Figure 17-9(b)

5.4 1

Figure 17-9(c)

356

Sec. 17-5

17-5 CYLINDERS

Cylinders

357

GIVEN: An object.

PROBLEM: Develop the flat pattern.

Figure 17-10 is an example of a problem that involves a cylinder.
Figure 17-11 is the development drawing derived from Figure 17-10
and was created by using basically the same procedure as was outlined
for Figure 17-2.

The stretchout length of the cylinder is equal to its circumference.
If, for example, the cylinder in Figure 17-10 had a diameter of 1.38,
the stretchout length of the flat pattern would be 4.33.

circumference = it diameter
C = n (dia)
= (3.14)(1.38)
= 4.33

If the cylinder size had been given in terms of its radius, 0.69 R,
the stretchout length calculations would have been

circumference - 2n radius

C = 2nR

= 2(3.14)(0.69)

= 4.33

The top and bottom surfaces of the cylinder in Figure 17-10 are
circles that ideally join the rest of the flat pattern at tangency points.
Tangency points are infinitesimal points that have no physical size and
are therefore impossible to manufacture. In reality, the top and bottom
surfaces of a cylindrical flat pattern are made separately and then joined
to the cylinder during assembly of the cylinder. For our study, assume
that tangency points can be manufactured and draw in the top and bot-
tom surfaces as shown in Figure 17-11.

DIA

Figure 17-10

SOLUTION:

Figure 17-ll(a)

c,d

a,b

Figure 17 -11(b)

358

Development Drawings

Chap. 17

Figure 17-ll(c)

Figure 17 -11(d)

Figure 17-1 1(e)

Figure 17-12 is a cylinder that contains an inclined surface. Figure
17-13 is the development drawing derived from Figure 17-12 by using
the procedure outlined for Figure 17-2. The orthographic views include
a partial auxiliary view of the inclined surface that was created by
using the procedure explained in Section 14-9 and is illustrated in Fig-
ure 17-14. As with the top and bottom surfaces of Figure 17-12, the
top and bottom surfaces join the rest of the flat pattern at tangency
points which we assume are possible to manufacture.

GIVEN: An object.

PROBLEM: Develop the flat pattern.

SOLUTION:

Figure 17-12

Figure 17-13(a)

359

360

Development Drawings

Chap. 17

TTD

Figure 17 -13(b)

ABCDEFGHIJKLA

Figure 17 -13(c)

ABCDEFGHIJKLA

Figure 17 -13(d)

Sec. 17-5

Cylinders

361

From Supplementary
Layout

Figure 17 -13(e)

Figure 17-1 3(f)

Figure 17-14 A supplementary layout used to derive the true
shape of the top surface.

17-6 PYRAMIDS

GIVEN: An object.

PROBLEM: Develop the flat pattern.

The flat patterns of pyramids are developed differently from the
patterns of prisms and cylinders. Figure 17-15 is an example of a prob-
lem that involves a pyramid and Figure 17-16 is the development draw-
ing. It was created by using the following procedure:

SOLUTION:

Figure 17-15

Figure 17 -16(a)

362

Figure 17-16(b) Use true length of line 0-1 ; see Figure 17-17.

Figure 17-16(c)

Figure 17 -16(d)

363

364

Development Drawings

Chap. 17

Figure 17 -16(e)

Figure 17 -16(f)

Draw as many orthographic views as are necessary to completely
define all surfaces of the object. Keep the views on the left side
of the drawing. Unfortunately, the orthographic views, as
presented, do not completely define the pyramid. We do not
know the true lengths of lines 0-1, 0-2, or 0-3, and therefore
we do not know the true shapes of the enclosed surfaces. To
find the true length of lines 0-1, 0-2, and 0-3, we may either
use the secondary auxiliary view method explained in Section
11-6 or the revolution method explained in Appendix A (il-

Sec. 17-6

Pyramids

365

True Length
of 0-1

Figure 17-17 A supplementary layout which uses the revolution
method to determine the true length of line 0-1.

lustrated in Figure 17-17). In this example the revolution
method was used. Regardless of which method you choose to
use, the important thing to remember is that you must know
exactly the true length of every line involved in the object.

2. Once the true length of all lines and the true shape of all sur-
faces have been determined, pick a point somewhere on the
drawing and label it point 0. From point draw an arc of
radius 0-1. Mark a point 1 on the arc, and then draw in (using a
very light layout line) line 0-1.

3. From point 1 draw an arc of radius 1-2. Obtain the distance
1-2 from the orthographic views. Label the intersection of the
large arc drawn from point and the arc drawn from point 1 as
point 2. Draw (using very light layout lines) lines 0-2 and 1-2.

4. In a similar manner, complete the layout of the pyramid's flat
pattern.

5. Erase all excess lines and darken in the periphery of the flat
pattern with heavy visible lines. Do not erase the lines that
represent the folding lines of the pattern. The point labels may
or may not be erased, depending on individual shop require-
ments.

This procedure may be used for any pyramid or cone problem.

366

Development Drawings

Chap. 17

GIVEN: An object.

PROBLEM: Develop the flat pattern.

Figure 17-18

Figure 17-18 is a pyramid problem that includes an oblique sur-
face. Figure 17-19 is the development drawing for the pyramid and was
created by using the same procedure that was outlined for Figure 17-15.
In this example we assume that the object has neither top nor bottom
surfaces.

SOLUTION:

ALL Distances From
Supplementary Layout

0-1 R

Figure 17 -19 (a)

Point 4

(MR

Point 3
Figure 17-19(c)

Figure 17 -19(d)

Figure 17 -19(e)

Sec. 1 7-7

Cones

367

As with other complicated problems, we may solve this problem
by thinking of it in terms of the simpler components problems that
comprise it. We can draw the basic flat pattern of the pyramid as was
done for Figure 17-15 and then mark off on each leg the distance that
represents the distance from the theoretical apex to the oblique sur-
face along that leg. To get these true distances, we start with the basic
orthographic views and by using the revolution method outlined in
Appendix A. For your convenience, the orthographic views, along with
the appropriate revolution method layout lines, have been redrawn in
Figures 17-20(a) and 17-20(b) so that you may see how each line was
drawn. These supplementary layouts are commonly used by draftsmen
to help insure accurate finished drawings.

Figure 17-20(a) Supplementary layout
used to determine the true length of all
the legs.

Figure 17-20(b)

17-7 CONES

Figure 17-21 is an example of a problem that involves a cone.
Figure 17-22 is the development drawing and was derived by using
basically the same procedure as was outlined for Figure 17-15.

A unique feature of cones is that they have no natural edges to use
as reference lines. To overcome this, we add theoretical lines as needed
and work from them as if they were, in fact, edges on the object. In this
example line 0-1 was added. Line 0-1 was located as shown because its
top view is parallel to one of the principal plane lines. This means that
its front view is true length (see Section 11-6 for further explanation).
We need the true edge length of the cone in order to develop the flat
pattern.

GIVEN: An object.

PROBLEM: Develop the flat pattern.

Figure 17-21

SOLUTION:

Figure 17 -2 2 (a)

The stretchout length of a cone's flat pattern, which is an arc, is
found by the following equation:

SL =

TEL

(360°)

(20-1)

where

SL = stretchout length
R = radius
TEL = true edge length

This equation yields a value for SL in terms of degrees. This means
that a protractor will be needed to lay out the SL value. The R/TEL
part of the equation is a proportion between the radius of the flat pat-
tern (equal to the true slant height of the cone) and the circumferential
base distance of the cone. By multiplying this proportion by 360 , we
can find out how many degrees of the full circle (360° } are needed for

Figure 17-22(b)

368

Sec. 1 7-7

Cones

369

Figure 17-22(c)

Figure 17-22(d)

the cone. In this example the slant height of the cone is 2.50 and the
radius is 0.75. Substituting these values into Equation (20-1), we obtain

TEL

(360°)

0.75
2.50

(360°)

= 0.30(360°)

= 108°

Therefore, the stretchout length, SL,

is equal to 108°.

370

Development Drawings

Chap. 17

PROBLEMS

Develop the flat pattern for the following objects. Dimension the flat
pattern. If assigned by your instructor, redraw the flat pattern onto
heavy paper or cardboard and then cut out the pattern and fold it up to
form a three-dimensional model.

17-1

17-2

2J00

17-3

1.75

1.00

17-4

1.13

2.13

1.00

17-5

Problems

371

1.25

2.38

< 1.31

17-8

.75

,94 R

17-9

1-25R

69R ^

100

^ t :

17-10

1.3a R

372 Development Drawings

17-11

.as rt

Chap. 17

2.75

17-12

2.50

1.00

17-13

.75 R

1.00

Problems

373

17-14

17-15

.68R

1.50

.75

30°

1.00

{

225

FINDING THE TRUE

LENGTH OF A LINE BY USING

THE REVOLUTION METHOD

APPENDIX

Define the line in at least two different orthographic views
[Figure A-l(a)]. In any one of the views revolve the line so
that it becomes parallel to one of the principal plane lines
[Figure A-l(b)].

In the accompanying illustration a line was drawn in the top
view parallel to the horizontal principal plane line through point
1 T and then point 2 T was rotated about point 1 T until it inter-
sected this line. The intersection of the line parallel to the
principal plane line and the rotation of point 2 T was labeled
point 2^ .

Project the point rotated in step 1 into the other orthographic
view so that it intersects a line drawn parallel to the principal
plane line through the other view of the point. A line drawn
from this point to the nonrotated point is the true length of
the line [Figure A-l(c)] .

In the accompanying illustration a line was drawn parallel to
the principal plane line through point 2 F and point 2' T was
projected into the front view so that it intersected the parallel
line as shown. This intersection was labeled 2 F . Line 1 F -2 F is
the true length of the line.

Top

/ 2 r

1 T

Front

2 T

/Indicates parallel lines

Figure A-l

374

App. A

Finding the True Length of a Line

375

Figures A-2 and A-3 are further examples of the revolution
method used to find the true length of a line.

Front

Side

Flgur* A-2

Sid*

Figure A-3

GAME PROBLEMS

APPENDIX

This section has been included just for the fun of it. Like most
skilled people, draftsmen enjoy games and puzzles that test and chal-
lenge their expertise; thus, they often try to stump one another with
game problems. Three have been included here for you to test your
skill. Try them and if you get stuck, write me and I'll send you the
answers. Have fun!

Top

Front

□

Side ?

Hollow object

Both are solid objects

Top

Front

Side ?

Figure B-l The two problems on the left side of the page are
missing view problems. The problem on the right side requires
you to draw 8 hollow objects stacked as shown. Remember all
the objects are hollow.

376

APPENDIX

DRAFTING ART

This section presents samples of drafting art. Draftsmen may use
their skill in geometric construction, line technique, and depth visualiz-
ation to create anything from geometric design to illustration. They are
limited only by their own imaginations and aggressiveness. Look over
the examples presented here and try copying a few. Then make up your
own creations.

Figure C-4

Figure C-5 (All straight lines.)

377

STANDARD
THREAD SIZES

APPENDIX

Whenever possible, a draftsman should call for standard thread
sizes in his designs. Standard threads may be purchased from many dif-
ferent manufacturers, are completely interchangeable, and are relatively
inexpensive when compared to "special" thread sizes.

Tables D-l and D-2 are the UNC and UNF standards. To find the
standard size for a given diameter, look up the diameter under the
desired thread {UNC or UNF) and read the standard thread size adjacent
to it. For example, a W-diameter thread UNC has 20 threads per inch.
The drawing call out would be

--20 UNC

A 1V4 UNF has 12 threads per inch and would be called out on a draw-
ing as

1^-12 UNF

The size numbers at the top of the tables are for small diameter
threads. For example a #4 UNF has a diameter of 0.112 and 48 threads
per inch. The drawing call out would be

#4(0.112)-48 UNF

Tables D-3 and D-4 define the 8 and 12 National (N) series thread.
In each case, all diameters in the series are made with the same number
of threads. All 8 series threads have 8 threads per inch. All 12 series
threads have 12 threads per inch. For example, a 1-7/8 diameter series
8 thread would have a drawing call out

l|--8UN

378

App. D.

TABLE D-l-UNC

Standard Thread Sizes

TABLE D-2-UNF

379

TABLE D-3-Series 8

TABLE D-4-Series 12

CD
£

Threads Pt
inch (P)

1 (0.073)

2 (0.086)

3 (0.99)

4 (0.112)

5 (0.125)

6 (0.138)

8 (0.164)

10 (0.190)

12 (0.216)

1/4

5/16

3/8

7/16

1/2

9/16

5/8

3/4

7/8

1 1/8

1 1/4

1 3/8

1 1/2

1 3/4

4 1/2

2 1/4

4 1/2

2 1/2

2 3/4

3 1/4

3 1/2

3 3/4

3 cj

(0.060)

1 (0.073)

2 (0.086)

3 (0.099)

4 (0.112)

5 (0.125)

6 (0.138)

8 (0.164)

10 (0.190)

12 (0.216)

1/4

5/16

3/8

7/16

1/2

9/16

5/8

3/4

7/8

1 1/8

1 1/4

1 3/8

1 1/2

CD
CD

5 cj

1 1/8

1 1/4

1 3/8

1 1/2

1 5/8

1 3/4

17/8

2 1/8

2 1/4

2 1/2

2 3/4

3 1/4

3 1/2

3 3/4

4 1/4

4 1/2

4 3/4

5 1/4

5 1/2

5 3/4

■21

CD O

1/2

5/8

1 1/16

3/4

1 3/16

7/8

15/16

1 1/16

1 3/16

1 5/16

17/16

1 5/8

13/4

1 7/8

2 1/8

2 1/4

2 3/8

2 1/2

2 5/8

2 3/4

2 7/8

3 1/8

3 1/4

3 3/8

3 1/2

3 5/8

3 3/4

3 7/8

4 1/4

4 1/2

4 3/4

5 1/4

5 1/2

5 3/4

380

Standard Thread Sizes

App. D

Pilot Drill Sizes for Coarse and Fine Threads*

Coarse (UNC, NC)

Fine (UNF t NF)

Nominal Thread

Threads

Pilot Drill

Threads

Pilot Drill

Diameter Per Inch

Diameter

Per Inch

Diameter

.073

No. 53

.086

No. 50

.099

No. 47

No. 45

.112

No. 43

No. 42

.125

No. 38

No. 37

.138

No. 36

No. 33

.164

No. 29

.190

No. 25

No. 21

.216

No. 16

No. 14

.250

1/4

No. 7

No. 3

.3125

5/16

.375

3/8

5/16

.4375

7/16

25/64

.500

1/2

27/64

29/64

.5625

9/16

31/64

33/64

.625

bfB

17/32

37/64

.750

3/4

21/32

11/16

.875

7/8

49/64

13/16

1.000

7/8

59/64

i.125

1 1/8

63/64

1 3/64

1.250

I 1/4

17/64

1 11/64

1.375

1 3/8

1 13/64

1 19/64

1.500

1 1/2

1 21/64

1 27/64

*from ANSB1. 1-1960

BIBLIOGRAPHY

Beakley, George C, and Ernest G. Chilton, Introduction to Engineering
Design and Graphics. New York: Macmillan, 1973.

Brown, Walter C, Drafting for Industry. South Holland, 111.: Goodheart-
Willcox, 1974.

Earle, James H., Design Drafting. Reading, Mass.: Addison-Wesley, 1972.

French, Thomas E,, and Charles J. Vierck, Engineering Drawing and
Graphic Technology, 11th ed. New York: McGraw-Hill, 1972.

Fryklund, Verne C, and Frank R. Kepler, General Drafting. Blooming-
ton, 111.: McKnight and McKnight, 1969.

Giachino, J. W., and H. J. Beukema, Engineering Technical Drafting and
Graphics, 3rd ed. Chicago: American Technical Society, 1972.

Giesecke, Frederick E., et al., Technical Drawing, 6th ed. New York:
Macmillan, 1974.

Grant, Hiram E., Engineering Drawing. New York: McGraw-Hill, 1962.

Hammond, Robert H., et al., Engineering Graphics. New York- Roland
Press, 1964.

Hoelscher, Randolph P., et al., Basic Drawing for Engineering Tech-
nology. New York: Wiley, 1964.

Hornung, William J., Mechanical Drafting. Englewood Cliffs N J ■
Prentice-Hall, 1957.

Jensen, C. H., and F. H. S. Mason, Drafting Fundamentals, 2nd ed New
York: McGraw-Hill, 1967.

Luzzadder, Warren J., Fundamentals of Engineering Drawing, 6th ed
Englewood Cliffs, N.J.: Prentice-Hall, 1971.

McCabe, Francis T., et al., Mechanical Drafting Essential. Englewood
Cliffs, N.J.: Prentice-Hall, 1967.

Nelson, Howard C, A Handbook of Drafting Rules and Principles.
Bloomington, 111.: McKnight and McKnight, 1958.

381

INDEX

Adjustable curve, 14
American Welding Society, 261
Ames lettering guide, 28
Angle, bisecting, 63
Arrowheads:

how to draw, 114

use, 113
Assembly drawings, 280
Auxiliary views:

partial, 231

projection theory method, 228-231

reference line method, 225-228

secondary, 232-240
no true length line, 240
Axonometric drawings, 316

Bolts:
how to draw hex heads, 258
how to draw square heads, 259
types, 255

Bosses, 198

Break lines, 286

Brush, drafting, 15

Cabinet projection (see Oblique draw-
ings)
Castings, 195-199

Cavalier projection (see Oblique draw-
ings)
Center line edge points, 171
Center lines, 26
Center point, 123
Centimeter (see Metric system)
Chamfers, 181
Compasses:

how to use, 10

leads, 11
Coordinate system (see Dimensioning)
Counterbore, 288-289
Countersink, 288-289
.Curves:

definition, 82

orthographic projection, 82-83

Curves (French), 12
Cutting plane lines, 206

Detail drawings, 282
Development drawings:

cones, 367

cylinders:
inclined prisms, 352
inclined surfaces, 359
normal surfaces, 357
oblique prisms, 354
pyramids, 362
rectangular prisms, 348

definition, 348
Dihedral angle, 149
Dimensioning:

aligned system, 123

angles, 124

baseline system, 125

common errors, 128

coordinate system, 126

holes, 123-124

hole-to-hole system, 126

irregular curves, 128

isometric drawings r 315

oblique drawings, 340

REF note, 130

rules, 114-122

sectional views, 214

small distances and angles, 125

tabular, 126

unidirectional system, 123
Dimension line, 113
Dimetric drawings, 316
Dividers, 15
Drafting art, 377
Drafting game problems, 376
Drafting machine, 14
Drawing detail, 287
Drawing zones, 284
Drilling, 288-289

Ellipse, how to draw:
approximate method, 62
four center method, 306-307

383

3S4

INDEX

Epoxy, 247
Erassrs:

gum, 3

types, 3

Erasing shield, 3
European drawing system (see First

angle projection)
Exploded drawings, 317
Extension lines, 113

Lines (cont.):
hidden, 90-91
how to draw, 38
intensity, 27
kinds, 26

orthographic projection, 77-80
principal plane, 74
tangency, 95
thickness, 26-27
true length, 233

Fasteners (non-mechanical), 247
Fillet:

between a circle and a line, 59

between two circles, 57

definition, 195

how to draw, 46-47
First angle projection, 272
Flat patterns (see Development draw-
ings)
French curves (see Curves)

Geometric constructions, general in-
dex, 36-37

Hexagon, 49-53

Hidden lines:
definition, 26, 90
rules for using, 91

Isometric drawings:
axis, 298
definition, 297
of holes, 306
irregular surfaces, 313
normal surfaces, 299
oblique surfaces, 305
round surfaces, 311
slanted surfaces, 302

Leader lines, 26, 113
Leadholders, 3
Leads, 3
Lettering:

freehand inclined, 27

freehand vertical, 27
Lettering guide, 29
Lines:

addition and subtraction, 39

base, 125-126

bisecting, 42-43

datum, 125

definition, 77

dividing into equal parts, 44

dividing into proportional parts, 45

drawing parallel, 40-41

guide, 28

Machine marks, 198-199

Magnifying glass, 15

Meter, 267

Metric system, conversion to inches:

definition, 267

mathmatically, 268

tables, 270
Millimeter, 267
Mitre line, 76
Models, 101

National Aircraft Standards, 261

Notes:

drawing, 284

fillets and rounds, 195

Object, 89
Oblique drawings:
axis, 325

cabinet projection, 326
cavalier projection, 326
definition, 325
holes, 335

inclined surfaces, 332
irregular surfaces, 338
normal surfaces, 327
oblique surfaces, 333
positioning, 335
round surfaces, 336
Octagon, 56
Ogee curve (see S-curve)
One view drawings, 284
Orthographic projection:
compound edges, 139-143
curved surfaces, 95
cylinders:

curved cuts, 178

cut above the centerline, 172

cut below the centerline, 174

eccentric, 184

holes in, 184

hollow sections, 186

inclinded cuts, 176
definition, 71
dihedral angles, 149-152
fillets and rounds, 195
inclined surfaces, 94
normal surfaces, 88

INDEX

385

Orthographic projection (cont.):
oblique surfaces, 144-147, 153-161,

162-164
parallel edges, 147-149

Paper:

graph, 97

grid, 97
Parabola, 64
Partial views, 284
Parts list, 283
Pencils (see Leadholders)
Pentagon, 54-55
Phantom lines, 27
Pictorial drawings, 297, 325
Pilot holes:

definition, 255

depth, 256

table of sizes, 380
Pitch (see Threads)
Planes:

definition, 80

orthographic projection, 80-81
Points, 38, 75-77
Principal plane lines, 74
Production drawings, 279-289
Projection rectangle, 76
Protractors:

how to use, 11

leads, 11

Quadrapads, 97

Reaming, 288-289

Revision blocks, 283

Revolution method, 365, 367, 374

Rivets:

detailed representation, 260

schematic representation, 260
Rounds:

between a circle and a line, 60

between two circles, 58

definition, 195

how to draw, 48
Runouts, 197

Sandpaper block, 3
Scales:

decimal, 4-5

fractional, 4

metric, 268
Screws:

how to draw hex heads, 258

how to draw square heads, 259

types, 255
S-curve, 61
Sectional views:

auxiliary, 231

Sectional views (cont.):

broken out, 212

counterbored hole, 289

countersunk hole, 289

definition, 205

drilled hole, 289

half, 211

holes in, 214-

iso metric, 315

location, 207

multiple, 210

oblique drawings, 341

reamed holes, 289

revolved, 211

threads, 253, 256
Section lines, 208
Ship's curve, 12
Sketching:

freehand isometric, 99

freehand orthographic, 97
Snake (see Adjustable curve)
Spot face, 198
Stretchout line:

cones, 369

cylinders, 357
rectangles, 348
Surface coloring, 101

Templates:

circle, 13

how to use, 14

isometric hole, 306
Thread representation:

schematic, 250

simplified, 249
Threads:

acme, 254

class of fit, 248

crest, 247

detailed, 251

double, 254

8 National Series, 378, 379

in holes, 255

knuckle, 254

left hand, 255

major diameter, 247

minor diameter, 247

notations, 248

pitch, 248

roots, 247

sharp-V, 254

square, 254

standard sizes, 378-379

terminolgy, 247

12 National Series, 379

UNF, UNC, 248, 254, 378, 379
Title block, 282
Tolerance:

buildup, 125

cumulative, 129

standard, 129

symbols, 129

386

INDEX

Triangles:

accuracy check, 7

adjustable, 317

for drawing section lines, 2U»

how to use, 7
Trimetric drawings, 316
T-square:

accuracy check, 7

how to use, 6-7
■ Two view drawings, 284

Welds:
callouts, 262
spots, 262
V-type, 262

Zones (see Drawing zones)

Visible lines, 26
Visualization, 88

AU.§. GOVERNMENT PRINTING OFFICE:2005-31 0-083/20379

PIN : 054076-000

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